A flight departs from Logan Airport's runway 27 over Boston Harbor. File photo

Construction of a 775-foot-tall skyscraper in Boston’s Winthrop Square would interfere with a busy Logan International Airport departure path and shift more flights to a runway that’s prompted complaints from residents in communities north and west of the city.

A tower taller than 710 feet would significantly reduce the capacity of the departure corridor for runway 27, wrote Stewart Dalzell, deputy director of environmental planning and permitting for Massport, in a letter to state environmental officials.

Building the 775-foot-tall tower would force airlines to shift more departures in northwest winds to runway 33L, in which flights depart over communities such as Chelsea and Somerville.

Residents and officials have objected to increased air traffic from runway 33L departures since 2013, when the FAA switched to a new GPS-based navigation system that concentrates flight paths over a handful of narrower corridors north and west of the city. In October, the FAA and Massport said they will study alternatives to the new flight patterns.

Millennium Partners has been designated as developer of the 1-acre municipal garage site at 115 Federal St. by the Boston Planning and Development Agency. Millennium proposes a 775-foot tower with 14 stories of office space topped by 36 floors of residential units and a ground-floor “Great Hall” with food vendors and public event space. Six developers submitted proposals last spring to the BPDA for towers up to 780 feet tall on the Financial District property. That exceeds the maximum 710-foot building height for the neighborhood in the FAA’s 2011 Logan airspace map.

Millennium Partners proposes a 775-foot-tall tower at 115 Federal St. in Boston’s Financial District.

“It was widely distributed among the development agencies including BPDA and the developer communities,” Dalzell wrote in a Dec. 22 letter to state Environmental Secretary Matthew Beaton.

Runway 27 departures already climb at an angle more than twice the standard gradient because of existing skyscrapers such as 600 Atlantic Ave., according to a graphic submitted with Dalzell’s letter.

Millennium and the BPDA also face a challenge to the tower’s height under a 1990 state law that limits shadows from new development being cast on Boston Common. Millennium Partners declined comment.