The dispute surfaced days before the Nov. 3 election. Minogue raised the issue in a weekend Facebook post, asking whether Healey had made a deal with the State Troopers for their endorsement.

At an event in Framingham on Monday, Healey said she was proud to have support from law enforcement groups, including four police organizations backing her campaign. She said that support reflected her work with law enforcement as attorney general and governor, and added that she stood by her administration’s work with police.

Brendan Murphy, president of the State Police Association of Massachusetts, said the allegation was “categorically false” and that the union stood by its endorsement of Healey. He also said accusing troopers of corruption without evidence was reckless and risked smearing their integrity and the contract they had earned for political gain.

Minogue said in a Monday statement that his concern was directed at Healey, not State Police troopers. He said troopers deserved a fair contract, competitive compensation and respect, and argued they should not face the perception that their contract could be linked to a political endorsement.

The disagreement puts the union’s endorsement and contract negotiations into the closing days of a statewide campaign. The governor’s race will be decided on Election Day, Tuesday, Nov. 3.