In the midst of a presidential election year when voters will also decide who controls Congress, one of the most heated campaigns in Montgomery County is an esoteric ballot measure about police officers’ bargaining rights.

The battle pits the county government against its police union. So far, the two sides have spent nearly half a million dollars trying to sway voters. And this week the issue, Question B on the Nov. 6 ballot, became so heated that the Maryland state prosecutor launched a criminal investigation into whether county officials improperly used county resources for politicking.

Meanwhile, the county has distributed fliers that read: “Who Do You Think Should Run the County Police Department? The Police Chief or Police Union Leaders?”

At issue is a decades-old provision known as “effects bargaining.” Montgomery police have the right to bargain over traditional issues such as salaries, benefits and working conditions.

But the police labor law also gave police the right to bargain over management decisions “which will have an effect” on officers. The Montgomery County Council deleted that provision last year.

Union officials, who gathered enough signatures to put the issue on the ballot, credit the provision with helping them secure important benefits, such as longer notice before schedule changes. But county officials say they must negotiate on decisions as basic as how to distribute time-saving ticket-writing devices.

Union leaders say they saw no need for a change, but county officials say one was needed to increase efficiency. Now voters will decide whether the council’s change will remain law.

According to the union, Fraternal Order of Police Lodge 35, the law unfairly limits its ability to bargain.

“Why overturn 30 years and cause such a ruckus among people up in the middle of the night taking 911 calls?” asked Lanny Davis, President Bill Clinton’s former special counsel, who was hired by the police union. “This is an age-old argument between unions and management. Why do I have have to sit down with the union? It’s my company. . . . This is really serious for a lot of cops. Is it worth it because the chief doesn’t want to be bothered?”

Davis also argued that even if his side loses, and the effects bargaining provision disappears, “the world doesn’t change for the police chief,” J. Thomas Manger.

“If this statute is repealed, there still will be litigation, argument and potentially arbitration over effects of directives by the management,” Davis said, citing the experience of other government employee unions in Montgomery.

But Manger said the change would help him better run the department. He has been the only police chief in Maryland subject to such an effects bargaining provision, he said.

“If the voters decide to eliminate effects bargaining, I will have the same level playing field that every other police chief in the state of Maryland has,” Manger said. He said he respects, and would continue to follow, the bargaining process. Even without effects bargaining, “there’s still going to be issues to be dealt with,” he said. But “we at least have a fighting chance of getting some of these through in a more efficient manner.”

Some officers fear the uncertainty of changing the long-standing provision.

About four months ago, union treasurer Matt Frasca found out that his 3-year-old daughter, Lucianna, has juvenile rheumatoid arthritis. Because his wife works as an administrative assistant, he takes care of Lucianna during the day, sometimes waiting at Johns Hopkins University for four hours so that his daughter can go to a doctor’s appointment.

Frasca works the evening shift. He said he knows that Manger could assign him to a new shift at any point. But because of union negotiations, the department generally would let him know three weeks in advance. This gives him time to adjust his family’s schedule.

County officials said the police union has other ways to negotiate on these issues. Union officials said the law could make bargaining more expensive and difficult, but they would invest whatever resources are needed to protect their members.

Manger said the fears are misplaced. Scheduling issues, for example, are outlined in the labor contract with police.

“No matter how this vote goes, I can’t go back and say all these sections in the contract are null and void,” Manger said. “This notion that all of a sudden I can just schedule people and transfer people on a whim is just not true.”

The union would not speculate on what changes would occur if voters endorse the changes made by the county council. Police managers pledged to bargain in good faith, though union leaders say they’re skeptical.

“All we’re asking is to maintain what we had and to be able to come to the table and to fairly discuss any change that they want to make,” said Denise Gill, a union steward, as she teared up in the Fraternal Order of Police office in Montgomery Village.

The debate has strained relations between the police department and the County Council. On one of the doors in the FOP office is a bumper sticker illustrated with a target that reads: “Montgomery County. Home of the County Council that AIMS to hurt working Police Officers.”

Over the past few weeks, the county has distributed fliers, sent out e-mails and created a Web site in support of Question B. The police union sought the inquiry by the state prosecutor. County officials said they have acted properly.

The union has hired two outside consulting groups, created its own Web site and gone on television to urge residents to vote against Question B.

As of last week, the county has spent $207,000 in legal fees and campaign materials on the referendum. The county board of elections has spent an additional $57,000 in legal fees. Meanwhile, the police union has spent $184,000 in legal fees and at least $25,000 in consultant fees.