What do Goldman Sachs CEO Lloyd Blankfein, actor Denzel Washington and Nascar driver Jeff Gordon have in common? An address.

Manhattan’s 15 Central Park West, just north of Columbus Circle, is one of the most exclusive—and expensive—addresses in a city full of exclusive, expensive residential buildings. The first of its 202 units hit the market in 2005 and sold out by the time construction was completed in 2007, raking in about $2 billion for the developers.

Today, the building continues to break price records as apartments hit the resale market. Many units have been elaborately upgraded and priced at more than double what owners paid for them a few years ago. In January, former Citigroup Chairman Sanford Weill sold his penthouse there for $88 million, making it the most expensive apartment ever sold in New York City, at more than $13,000 per square foot. (The average Manhattan condo sells for about $1,300 per square foot, according to Prudential Douglas Elliman’s most recent Manhattan market report.)

Some real-estate observers say that despite a record of stratospheric sales, asking prices today in the building have gotten overeager. While the average price per square foot in the building continues to rise, sales volume has slowed in the past few months, says appraiser Jonathan Miller. So far this year, five apartments have sold, compared with 17 last year and 15 in 2010, according to data from Brown Harris Stevens.

Rick Kelly, a broker with Prudential Douglas Elliman, says some of the pricing there today is tied to an “irrational exuberance” over the past few months about the building and the high-end market in general, with roughly $4,500 to $7,000 per square foot a more realistic price for units on lower floors without park views and no outdoor space, and $8,000 to $10,000 per square foot for apartments on higher floors with park views. With seven units currently for sale in the building, “there’s room for negotiating,” he says.

That hasn’t deterred some residents from setting ever-higher prices in the wake of Mr. Weill’s record-setting $88 million sale. Steel magnate Leroy Schechter has priced two combined units on the 35th floor—the units are still under construction—at $95 million, or $15,835 per square foot. He still hasn’t gotten any takers. (Emily Beare, Mr. Schecter’s listing broker, says she plans to begin fully marketing the apartment in January, once it is complete.)

Ms. Beare acknowledges pricing the work-in-progress apartment “was tricky.” The unit is 700 square feet smaller than Mr. Weill’s and does not include outdoor space. But unlike Mr. Weill’s penthouse, it includes panoramic views of Central Park and the Hudson River, compared with park and interior-courtyard views. Slated for completion in January, it has its own elevator landing and includes an apartment that Yankees third baseman Alex Rodriguez rented for a time. Mr. Schecter says the price is justified because there isn’t anything similar currently on the market and “it’s the only building of its kind.” The nearly 6,000-square-foot apartment will have five bedrooms, including a master suite with a sitting room and dressing area, seven bathrooms and two separate laundry rooms.

One high-price listing was just taken off the market. In September, two adjacent units on the 24th floor with a total of roughly 4,000 square feet were listed for $44 million. Last week, the seller decided to delist them, and one is now available for rent at $38,000 a month. According to public records, the apartment is owned Neil Witriol, the retired president of a company that makes steam baths and showers. He paid $7.8 million for the first unit in 2008. Listing broker Roberta Golubock, of Sotheby’s International Realty, says that unit has been gut renovated and includes a bathroom with chromotherapy showers (so the owner gets bathed in light as well as water). He paid $8.9 million for the second unit in 2010, which he is currently leasing.

The least expensive apartment available in the building: a 1,900-square-foot, two-bedroom apartment on the 16th floor asking $8.5 million, according to StreetEasy.com.

Broker and luxury-market tracker Donna Olshan says many residents at 15 Central Park West have spent upwards of $1,500 per square foot on gut renovations and upgrades to the relatively basic fixtures that came in units purchased from the developer.

The building now faces some competition in the neighborhood. Under construction a few blocks away are two ultra-high-rise, ultra-high-priced buildings also attracting billionaire and multimillionaire buyers, including many from overseas. Developers of One57, a 90-story building across from Carnegie Hall with views of Central Park, say two buyers are in contract to pay more than $90 million for two apartments. The former site of the Drake Hotel on Park Avenue is slated to become a nearly 1,400-foot-tall ultra-luxury condominium. It includes a penthouse marketed for $85 million.

William Lie Zeckendorf, who developed 15 Central Park West with his brother, Arthur, says in general, he thinks units in the building on the market today may actually be underpriced. Unlike the coming high-rises, his building is directly on Central Park and already built. “I think the building is frankly so much better than what’s out there,” he says. “I think the prices should be higher.”

The Zeckendorfs were met with widespread skepticism when they began developing the building nearly a decade ago. In 2003, they paid $401 million for the Mayflower Hotel and a surrounding lot—a record price for a development site at the time. William Zeckendorf says they modeled the project somewhat after another building they did at 515 Park Ave., known for its old-world look, modern amenities and generous floor plans. With 15 Central Park West, he says, they decided to make the apartments even larger and the building’s amenities even grander. “We were trying to fill a segment of the market we felt had been under-built for 30 to 40 years in Manhattan,” he says.

They hired architect Robert A.M. Stern to create the design, which Mr. Zeckendorf says they closely oversaw themselves, meeting with Mr. Stern or his office five to six times a week for a year to discuss layouts, amenities and finishes. The result is a towering building clad in limestone with a formal oak-paneled lobby and grand columns; the building is meant to evoke the city’s classically grand prewar buildings.

The complex is actually made up of two connected buildings, or wings, because of zoning restrictions. The front building, known as “the House,” has 20 stories overlooking Central Park and is home to celebrities like rocker Sting and his wife, Trudie Styler. It also includes Mr. Weill’s former apartment, which was purchased by a trust linked to Ekaterina Rybolovlev, the 23-year-old daughter of Russian fertilizer billionaire Dmitry Rybolovlev. In the back is “the Tower,” a 43-story building that, on its upper floors, includes both park views to the east and Hudson River views to the west. Average apartment size in the complex: roughly 5,500 square feet.

Owners also have access to a private 14,000-square-foot fitness center, an indoor swimming pool and a screening room. With a full-time staff of more than 50, the building also has two separate entrances, including an old-world-style gated motor court. The building also includes 29 smaller “suites” designed as separate quarters for staff, guests or home offices, available for purchase only to residents. Some have sold for upward of $2 million. Also available for residents to purchase are roughly 30 climate-controlled wine rooms with access to a central tasting area; none are currently available.

The building also has a private restaurant open only to residents and their guests—one of only three such establishments in the city, and the first built in more than 50 years, according to the developers. The menu ranges from burgers and fries to a more formal seasonally rotating menu, also available as room service.

The building’s board of directors has set strict rental restrictions, allowing owners to rent their units for just one year at a time with no guarantee of a lease renewal without board approval; renters aren’t allowed to have pets or smoke in the building, according to brokers familiar with the policies. They also, of course, face steep price tags. Mr. Kelly, of Prudential Douglas Elliman, says there are five apartments for rent in the building, including a 2,700-square-foot, three bedroom unit for $40,000 per month in a midlevel floor with park views. Additional fees include 5% of the monthly price for building wear-and-tear, plus a standard Manhattan broker’s fee of 15% of one year’s rent.

But for some, there’s the hope that paying such a premium might pay off. “Business deals get done on cocktail napkins there,” says Mr. Kelly. “I think a big draw on the rental side is that proximity.”