A rendering of the New York Methodist Hospital's planned Center for Community Health, which a Park Slope group is opposing in court. New York Methodist Hospital

A Park Slope community group filed a lawsuit on Wednesday to block a 485,000-square-foot outpatient center by New York Methodist Hospital, creating a hurdle for a growing hospital in a borough where most of its counterparts are struggling to survive.

The addition, between Fifth and Sixth streets and Seventh and Eighth avenues, would include 12 operating rooms for same-day surgery, a cancer center, an endoscopy suite and an after-hours urgent-care center.

The suit was filed by Preserve Park Slope Inc., a group formed in reaction to the proposal. It is challenging a zoning variance that was granted in June by the Board of Standards and Appeals. It says the city administrative body overstepped its authority.

"I think we have as strong a case as I've ever seen coming out of the BSA," said Albert Butzel, the attorney for the plaintiffs, referring to the city standards and appeals board.

A representative for the Board of Standards and Appeals declined to comment, citing the pending litigation.

Among other objections, opponents say the modern addition of stone, glass and steel would be out of scale and character with the surrounding brownstone neighborhood.

A spokeswoman for Methodist Hospital said the hospital had made more than 20 changes to the project based on community feedback, including reducing its height along Eighth and Fifth avenues and adding a rear yard to provide more light, air and green space.

"We are disappointed that a small, special-interest group has chosen to ignore the land-use process and file this suit," she said. "It could delay construction of the Center for Community Health, a facility that will bring much-needed access to cutting-edge outpatient health care to Brooklyn residents. We believe the suit is without merit."

The hospital estimated the facility would accommodate about 100,000 additional outpatient visits a year.

A 2003 rezoning that restricted development in parts of Park Slope included the area that surrounds the hospital. The city allowed Methodist to expand on certain sites in the area, in exchange for which the hospital would agree to abide by the more restrictive zoning in other parts of the neighborhood, the lawsuit says.

The hospital spokeswoman said there was no such agreement as part of the 2003 rezoning.

The hospital sought an exemption to the zoning from the standards and appeals board, which approved the change unanimously.

The project has riled certain community members because the hospital would need to tear down 16 buildings that are all roughly four stories.

Opponents say that the project will lead to the loss of some 100 units of housing, but hospital officials said that many of them are now used as back-office space for New York Methodist or are vacant.

The hospital said residents would be relocated to equivalent housing.

Simeon Bankoff, executive director of the Historic Districts Council, said in a sworn affidavit provided by the plaintiffs that the project looked like "a corporate office park."

Opponents say they aren't opposed to any expansion by the hospital, but they want to see the building—now designed at six to eight stories—cut down in height.

"It is a residential, beautiful, historic community. What Methodist plans will disrupt that tremendously," said Marvin Ciporen, a resident of the area for more than 41 years whose first grandson was recently born at Methodist Hospital. He is one of the plaintiffs in the lawsuit.

If the lawsuit is successful, it would invalidate the standards and appeals board's decision and could prevent the project's construction, which the hospital hopes to begin this year.

Write to Laura Kusisto at laura.kusisto@wsj.com