A project connecting offices for Google in two Boston Properties buildings will begin next month, the company said. A legal report on how the project came to a vote is set to be heard in two months.

There will be a legal review of actions taken over the past couple of years by the executive director and staff of the Cambridge Redevelopment Authority, but the project sparking demands for that review — the structure developer Boston Properties is building at the cost of a rooftop garden in Kendall Square — is getting under way before the report comes back.

At the Wednesday meeting of the authority’s board, chairwoman Kathleen Born asked officially for a report at the next meeting concerning the legality of those actions. But that meeting is scheduled for September, while representatives of Boston Properties reported that work on its project would start in August.

“The fact is, based on the City Council’s approval … this is the area we’ll be working with,” Boston Properties project manager Kevin Sheehan said.

This cuts to the heart of the complaints of residents such as Steve Kaiser, who has spoken repeatedly at meetings of the authority with references to the “illegal” actions of the past two years: The council voted 7-2 on March 19 on a plan by “Boston Properties, together with the Cambridge Redevelopment Authority” when the authority’s bylaws say that is impossible: The authority had no active board members, and Executive Director Joseph Tulimieri has only administrative powers based on the direction of board members.

The authority is looking at whether laws were broken in crafting the proposal voted on by the council. Meanwhile, Boston Properties justifies construction by citing the council’s vote.

The review will look at actions between September 2009 and May 2012 “and evaluate whether appropriate votes and procedures were taken during that time and followed in the absence of a full quorum,” Born said, “and then I’ve asked counsel to make a recommendation whether any action by the current board might be necessary or appropriate in light of that review.” The authority’s counsel is Jeffrey Mullan, of the law firm Foley Hoag.

After spending the better part of an hour discussing the size and kind of signs being put up in Kendall Square, the discussion of legal review all took place within a couple of minutes.

Born reminded the audience for the Wednesday meeting that she had promised the board would look back at authority actions of the past two years “as necessary.” The wrestling over the design plans for the rooftop garden — which will connect offices for Google in two Boston Properties buildings, creating two floors of wide-open space for the Internet search giant — is part of that review. Boston Properties officials haven’t given a formal response to the board’s design suggestions, even as work begins next month.

Board member Chris Bator wondered at the timing.

“It seems to me that if you’re already fencing off portions of the garden you’re taking, it renders somewhat moot responses to the design comments we’ve had. It treats it as an exercise of form over substance,” Bator said.

The fence would be installed no matter what design points the board has to make, Sheehan responded, since the council’s vote returned chunks of the garden to Boston Properties control.