Image courtesy of The Architectural Team

Construction of an $80 million hotel next to Boston’s Rose Kennedy Greenway is being challenged by a North End neighbor who argues that a proposed enclosed roof deck would exceed maximum zoning heights.

Developer Cross Street Ventures received approval from the Boston Planning & Development Agency in March to redevelop the former J. Pace grocery market property at 42 Cross St. as a 134-room hotel.

The development would cast shadows and restrict air flow to Mary Beth Sweeney’s property on Stillman Street, according to the lawsuit currently under review in state Land Court. It names developer Cross Street Ventures and property owner J&A Realty Trust as defendants.

The BPDA approved the project in March despite opposition from some North End residents and state Sen. Lydia Edwards. The project also requires approval by the Boston Zoning Board of Appeal for variances related to floor area ratio, rear setback and rooftop restaurant, and conditional use permits for the hotel and first-floor restaurant uses.

The plans include a roof deck including a restaurant atop the 55-foot-tall hotel, which the suit argues would increase the building height by 12 feet, requiring an additional height variance.

Lawyers for the developers submitted a motion to dismiss on July 1, arguing that the lawsuit is premature because the ZBA hasn’t voted yet on the project. They also challenged the jurisdiction of the case, arguing that it should be argued in Suffolk Superior Court.

In a response filed Aug. 1, Sweeney’s attorney said the height variance is a legitimate legal issue because the Boston inspectional services department issued a letter of refusal on May 20 and the developer refuses to acknowledge that a height variance is needed.

The ZBA is scheduled to review the project on Aug. 23.