County Comptroller George Maragos, who has been trying to audit the Clinton G. Martin Park District in New Hyde Park since 2011, said residents claim park funds were misallocated.
But the audit has stalled in the courts while the town challenges the county's power to perform such a review. Kaiman has called it "unconstitutional."
The courts have largely disagreed, and the state Court of Appeals last month denied an automatic appeal request after two lower courts ruled against the town.
In the past two years, the county and town have openly clashed.
Kaiman then referred to the back-and-forth as a "political circus."
But in an interview Thursday, Kaiman said the disagreement had "taken on a life of its own," and said further challenging the audit could highlight a perception that the town has something to hide.
"It does come to a point where we want to get the substantive issue resolved: why they wanted to have the audit in the first place."
Of that matter, Kaiman said: "The documentation will speak for itself."
The move comes more than two weeks after the court of appeals' decision, and a month after GOP Councilwoman Dina De Giorgio announced her bid for supervisor. Kaiman said he was not ready to make any announcements about whether he will seek re-election, and the town Democratic Party said last month its slate would be decided by the county's convention on May 28.
Jostyn Hernandez, a spokesman for the comptroller, said Maragos "thanks Supervisor Kaiman for the note he received asking us to audit them."
Though the courts confirmed the county's right to audit a town district, Hernandez added the review will be simply "on the Clinton G. Martin Park, which has been our focus for the last two years."
Kaiman said the town still plans to follow up with another motion to appeal, but there is an uphill climb: the court can choose not to take the case. "We still want the legal issue to be resolved," he said. "But we don't know when that might be."
Kaiman said the audit will start next Thursday, with an entrance conference -- a meeting between auditor and representatives of the entity being audited.
When asked if there was an official mending of fences, Kaiman said of Maragos: "He and I have no personal dispute. It's really been one of principle and form."
He added: "We think they'll have a better idea of what we're talking about when we show them what's going on."