The new board of the Cambridge Redevelopment Authority is meeting next week — but at exactly the same time as the City Council meets, putting people most interested in the doings of city officials in a bind as to which meeting would be best to attend.

The authority, which has been shaping Kendall Square since 1955, has been without a board for two years but has gone on conducting business in apparent violation of its bylaws. City Manager Robert W. Healy presented the council with four new board members April 9, and the state’s board member has said he is similarly ready to work.

A message was left Wednesday asking the authority’s executive director, Joseph Tulimieri, why the meeting was scheduled for 5:30 p.m. Monday, the same time as the council meeting. The meeting is at the Marriott Hotel, 2 Cambridge Center, in the third-floor Endeavor Room. The three-page agenda only starts with such things as election of officers and determining how public comment will be handled.

Among the first steps to be taken by the board members must be a review of what Tulimieri was working toward in their absence, including the deeding of ground-level park land along Binney Street and the train tracks and a plan by developer Boston Properties to build atop a rooftop garden to connect buildings housing Google offices. Tulimieri also approved some construction and the installation of a large sign for Microsoft and set in motion plans for Cambridge’s “gateway” from Boston at the Longfellow Bridge.

Whether Tulimieri’s work was legal is to be addressed at a June 5 meeting of the council’s Government Operations and Rules subcommittee, said David Maher, the subcommittee’s chairman, after the April 30 council meeting. Although he said the June meeting’s primary interest was in looking at “what the council’s role with the Cambridge Redevelopment Authority was … and there really isn’t a role, it’s governed by the board of directors,” Maher also acknowledged that he didn’t know whether the actions of the agency over the past two years — when there was no board — was legal.

“I’m sure it will be addressed,” Maher said.

The city’s Law Department is responsible for determining whether the actions of the authority over the past two years fit with its bylaws, said a communications specialist at the state Department of Housing and Community Development, Mary-Leah Assad.

One member of that subcommittee is councillor Minka vanBeuzekom, who wrote the policy order asking for a definition of the council’s role in the running of the authority. Maher’s quick answer last month indicated that he feels that aside from confirming Healy’s appointments to the board, there is none.

But on April 9, councillor Ken Reeves hoped that the subcommittee would look into the council’s role while linking those hopes directly to “how the CRA could be operating without a full complement of people, how the CRA could be holding meetings.”

“We really need a deep review of the CRA going forward and going backward,” Reeves said. “This has not been a good show of how we could best do business.”

Noting the possibility that appointment might be the council’s only power over the authority, councillor Craig Kelley suggested that the new members’ confirmation be put off until after an examination of the authority. He lost that vote 8-1, with even vanBeuzekom and Reeves voting in favor of the immediate appointments.

This post was updated June 7, 2012, to correct that Maher spoke after the April 30 council meeting about legal review, not after the meeting a week earlier.