Boston Properties’ plan for a rooftop connector building for Google must be approved by new Cambridge Redevelopment Authority board members.

The Google connector building approved by the City Council last month could yet be stalled or ended. In addition to having approval over how it gets built, the five board members of the Cambridge Redevelopment Authority also decide whether it gets built, said the authority’s executive director, Joseph Tulimieri, on Tuesday.

The building proposal was rushed through a resident review process and council vote between Feb. 27 and March 19 by Google’s landlord, developer Boston Properties, after Tulimieri signed off on it for the authority. But he acted without the board, which was empty; now there’s an active state member and the city manager presented four city members to the council Monday, with all winning council approval.

And that connector building, which will result in residents losing 40 percent of a treasured rooftop garden, looks to be the top priority for the new board, given that City Manager Robert W. Healy presented the plan as having “a timeliness.”

“Google is a very good tenant to have, and I think there’s going to be a predisposition to see what we can do to assist Boston Properties in retaining Google in a rather dramatic presence — we’re talking 300,000 square feet of space by a first-class firm,” Tulimieri said in a telephone interview when asked about the plan. “Can the authority say, ‘No, we don’t want it’? Sure. The authority could do that. I’m not going to speculate as to whether they should do that.”

Although the authority’s bylaws say only that as executive director he has “general supervision over the administration of its business and affairs, subject to the direction of the authority,” Tulimieri insisted he acted within his powers in developing the plan with Boston Properties for Healy to present to the council.

“There were no actions taken that would require a board action — there was no land that was disposed of, no land acquired. There were certain actions taken on the staff level that are the normal actions taken in the staff level,” he said. To anyone thinking the bylaws say differently, he said, “That’s your interpretation of the bylaw, which doesn’t happen to be mine.”

On a similar matter — approval of a giant sign for Microsoft that has been installed atop the very Boston Properties building in which the authority keeps its offices — he suggested that the bylaws have to be reinterpreted to fit changing times:

“When those bylaws were written, there was no issues involving signs. There’s going to be nothing in those bylaws with respect to signage. It’s fundamentally an operating issue of the authority. Whether or not there’s development that takes place, that’s clear in the bylaws as to what the authority’s chartered to do. It doesn’t say ‘All signs shall be Helvetica and cannot exceed [a certain height] or be backlit. There’s none of that there. As a part of the development process … there is likely to be some signage that will be proposed and reviewed. Within that context, the signs will be reviewed by the authority. If the authority doesn’t like the sign, the sign gets changed.”

He also wanted to correct two misperceptions in the community, media and members of the council, the first being that he acted alone to deed property in the years since there has been a quorum of the board empowered to take action. In particular he said there has been no actual deeding of future parkland along Binney Street, some of which stretches along a sidewalk and a connecting portion of which has been referred to as “pork chop” shaped, which Boston Properties has promised to develop for up to $2 million in exchange for the connector building.

The second misperception: That the authority is intended only to act in Kendall Square and has an expiration date as an agency when Kendall’s parcels are filled. “The CRA goes on for as long as the CRA determines it goes on. If the authority is to be dissolved, it requires a vote of the authority, not a vote of the City Council.” Meanwhile, he said, “between now and the completion of Kendall Square, the city manager and City Council could make a determination that it wishes to have an entity with powers of the authority involved in another redevelopment project — at NorthPoint, at Alewife …”

While Tulimieri confirmed he is technically retired — he works part time at the authority, keeping with a required 960 hours a year, he said — he said he intends to go on as executive director as long as the board keeps him aboard.

That board’s five members will have an orientation as soon as possible, Tulimieri said, as soon as he gets the new members’ contact information and gets them to take the oath of office. Then the board will meet, with notice for the public “duly posted at the city clerk’ office 48 hours in advance.”

Attempts were made Tuesday to reach the new board members. Kathleen Born referred all questions Tuesday to Tulimieri; a message was left with former city clerk Margaret Drury; the remaining members, Chris Bator and Conrad Crawford, do not have listed phone numbers. One attended Monday’s meeting of the council, where diversity among appointees — Healy confirmed one member is black — took up more time than their confirmation vote, despite the weeks-long controversy concerning the authority and Boston Properties proposal.