With union leaders, hospital workers, and a cadre of police officers looking on at Woodbridge Hall, organizers for Yale-New Haven Hospital employees seeking to form a union presented on Thursday a petition asking Yale and the hospital for neutrality.

The petition, which requested that the Yale Corporation and the board and officers of Yale-New Haven Hospital “forge a new partnership with us,” carried the signatures of 1,190 hospital workers, said Deborah Chernoff, a spokeswoman for the Federation of Hospital and University Employees. The federation includes Yale’s recognized unions — locals 34 and 35 — as well as Service Employees International Union District 1199, the group attempting to unionize the hospital workers.

The petition called for a card-count neutrality agreement, under which hospital officials would agree not to express opinions on unionization, and allow a union to form if a majority of workers signed union cards. Chernoff estimated the number of workers eligible to vote on unionization would be about 1,800, but added she could not be sure because hospital officials would not release the information.

Union leaders had asked to present the petition to Yale President Richard Levin, but Levin was not available. Nina Glickson, an assistant to the president, agreed to receive the petition instead.

Union leaders also delivered a copy of the petition to labor relations officials at Yale-New Haven after receiving no answer to requests to deliver the petition to hospital CEO Joseph Zaccagnino.

The presentation of the petition comes as part of a more than two-year-long effort by District 1199 to unionize the hospital workers, and three weeks into negotiations between the University and its two largest recognized unions over contracts for nearly 4,000 Yale workers.

Leaders from locals 34 and 35 have said recognition for the hospital workers and graduate students trying to organize should be addressed in the contract negotiations.

Levin has repeatedly said that he does not oppose unionization for hospital workers, but that he does not control the hospital and cannot recognize the hospital workers as a union. Glickson repeated Levin’s position to Dave Pickus, a vice president of the New England Health Care Employees Union, after he gave her the petition Thursday.

“The president has said he has no authority over the hospital,” Glickson said after receiving the petition.

“We appreciate him staying out of it, but he’s in it,” Pickus responded.

Pickus added that the Yale Corporation could influence the hospital, and that recognition of the hospital workers was a necessary condition for the new tone in labor relations Yale and union leaders have said they are hoping to achieve.

Clayton Medeiros, a senior vice president of Yale-New Haven Hospital, said the hospital would abide by the rules of the National Labor Relations Board, and opposed neutrality.

“Our position has not changed,” Medeiros said. “There’s not much to be said about it.”

But the union leaders and hospital workers who gathered outside Woodbridge Hall said they were hopeful the group would be recognized, and added that the effort was a sign of unity between the different unions in the federation.

“The bottom line is the community is coming together,” said Shirley Lawrence, a member of Local 35 who came to support the hospital workers. “These people are our sisters and brothers, our relatives. We’re encouraging them to fight for what’s right.”