One day after the union seeking to organize Yale-New Haven Hospital withdrew its petition for a union election, the state of affairs between union organizers and the hospital’s high-level administrators is, in one word, nebulous.

Interviews with more than a dozen workers, hospital leaders, members of the hospital’s Board of Trustees and local political observers reveal marked disagreement as to who, if anyone, might be guilty of violating the neutrality agreement designed to ensure a fair up-or-down vote on the union last December. As independent arbitrator Margaret Kern wraps up her investigation this week and prepares to issue a ruling, there are more questions than before as to what the future will bring for both sides.

The union’s decision to withdraw its petition to the National Labor Relations Board for an election may suggest that union leaders no longer think they would be able to win a two-day election. SEIU 1119 union leaders have declined to produce the document they claim implicates several top hospital managers, saying that they must wait to do so until after Kern issues a ruling.

Two weeks ago, hospital CEO Marna Borgstrom EPH ’79 was called to testify before the arbitrator, but Borgstrom has declined to comment on her role while arbitration is still underway. On Tuesday, she was approached by a News reporter outside her office to comment on the alleged document.

“I’m not going to have a conversation about that,” Borgstrom said. “Arbitration is still going on.”

But hospital Senior Vice President Dr. Peter Herbert, who praised Borgstrom for what he said was her unmatched ability to find common ground, said he had seen some training materials put together by consultants hired to advise hospital administrators on dealing with the union.

“I think a small amount of the material, though none of it was illegal from a NLRB point of view, some of it was certainly more negative about organized labor than we would have intended,” Herbert said, adding that none of it was ever used. “I think there is no question, the hospital made some mistakes as to what the expectations were of the arbitrator.”

He said the document had talking points that “would not be something that we would do in the campaign,” but that “we are still responsible for any materials that are distributed to the managers.”

It is typical for a hospital to hire a consulting firm to figure out how best to convey a hospital’s message to employees while remaining within the confines of the law.

Hospital Chief Operating Officer Richard D’Aquila EPH ’79, who works side-by-side with Borgstrom, declined to comment, hanging up the phone upon learning that the caller was a reporter.

Workers at the hospital on Tuesday had mixed views as to whether managers actually partook in the intimidation alleged by the union since last December.

From his food kiosk in the hospital plaza, Michael Bobb said that the union’s allegations are mere “propaganda” and that Borgstrom — whom he said is well-liked by almost all hospital employees, “top to bottom” — is not pro- or anti-union as much as she is “pro-hospital.”

“There is no such document whatsoever,” he said. “It’s their game.”

About half a dozen workers agreed with Bobb that the union was stretching the truth. But another worker, who wished to remain anonymous because said she had gotten in “trouble” previously for pro-union comments, said she had witnessed intimidating meetings and other propaganda tactics on behalf of the hospital.

“They intimidate us … a lot,” she said before whispering that she had to leave because a manager was approaching.

A hospital employee, who declined to give his name, made reference to a specific event he said indicated to him that the hospital was violating the rules set out for the election. In early December, he said, some managers held a mandatory meeting that became optional in name only at the end, when someone described as a former union employee at a New York City hospital began to discuss his personal experiences with unions, aiming to persuade Yale-New Haven Hospital workers to vote against forming one.

Hospital spokesman Vin Petrini said IRI Consultants to Management, the firm hired to advise the hospital in preparation for a vote, may have played a part in such meetings but the company, as of December, does not work with the hospital. On IRI’s Web site, there is no mention of unionization issues, but a document available on the site promises to help executives “improve communication, trust, and cooperation throughout the organization.”

Throughout the city, there are additional questions being raised beyond the merits of the document that has been described by the union: why the union pulled out of the secret ballot election and what that means for its future.

According to SEIU spokesman Bill Meyerson, it’s a matter of trust.

“They destroyed the possibility of an election, they denied that they did anything wrong,” he said. “How can people like that be trusted, regardless of what they agree to?”

But some workers and administrators said SEIU may have pulled out because they concluded they would not be able to succeed in an unionization vote.

The union is now demanding a card-check election, in which it is significantly more likely that a union will be formed. The process is not limited by time, as a union is created as soon as 50 percent of workers sign union cards.

Although Yale President Richard Levin, who sits on the hospital’s Board of Trustees, supported a card-check election at a labor dispute involving workers at the Omni Hotel several years ago, he said he does not think it is an appropriate solution at the hospital.

“The problem with card check is, I think, that it is a fundamentally anti-democratic,” he said. “I know from my days at graduate school people who had signed cards because of social pressure. If people are coming to your house every night for three weeks until you sign, you can’t be free of the pressure.”

Around the city, there is no consensus as to who is at fault or what should be done next. Although the members of the Board of Aldermen have generally expressed distaste for the hospital’s alleged actions, the resolution they passed several months ago did not single out one side. At the time, Ward 18 Alderwoman Arlene DePino, the only Republican on the Board, even said she had personally witnessed intimidation on behalf of the union when a union advocate stuck his foot in a door and refused to leave.

But Mayor John DeStefano Jr. has been clear that he thinks the hospital is in the wrong, which, according to Herbert, is something Borgstrom is quite upset about. He said she is stuck “between a rock and a hard place.”

“She’s very unhappy with where she is right now,” Herbert said. “She’s very unhappy with the current relationship with the mayor, and she would like to find a way to bridge that gap. Both the mayor and Mrs. Borgstrom have expended a lot of political capital over this.”