The head of the New York City Campaign Finance Board on Wednesday dismissed an ethics complaint against Mayor Bill de Blasio’s fundraising nonprofit, but lamented that acceptance by such groups of unlimited donations, “plainly raises serious policy and perception issues.”

Board chairwoman Rose Gill Hearn and a coalition of good-government groups called for a new law to regulate nonprofits such as the mayor’s Campaign for One New York, which legally raised hundreds of thousands of dollars from organizations with business before the city.

“It defies common sense that limits that work so well during the campaign should be set aside once the candidate has assumed elective office,” she said.

“The board will not allow candidates to sidestep contribution and expenditure limits by outsourcing essential campaign activities to these coordinated organizations,” she said.

In dismissing the complaint, the board said it would have viewed the probe into the nonprofit differently had it concerned activity in a candidate’s election year — in the case of de Blasio, in 2017. But the conduct at issue occurred outside that time frame, the board said.

Under city law, a contributor to a mayoral campaign may donate up to $4,950 in the election cycle if the person isn’t doing business with the city — but only $400 if the donor does business with the city.

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De Blasio’s nonprofit, which pushed his policy agenda on issues including housing and universal prekindergarten, accepted donations far in excess of those limits. At least a dozen were as large as $100,000, Gill Hearn said. Such nonprofits legally can collect unlimited amounts.

Wednesday’s ruling was prompted by a complaint by the nonprofit good-government group Common Cause whose executive director, Susan Lerner, said the case exposes “a real gap in our campaign finance laws.”

“We have a public policy here in our city about large campaign contributions: We don’t allow them. We don’t allow a pay-to-play atmosphere and the mayor has gone around that, and there’s no excuse for that.”

De Blasio and his inner circle are the subject of at least five probes by city, state and federal investigators. Several of them center on Campaign for One New York.

Lerner said, “the onus is now on the City Council to close this gap and on the mayor to sign a bill if it’s passed.”

The good-government groups have proposed bringing nonprofits such as the Campaign for One New York under the jurisdiction of the Campaign Finance Board.

In a statement, a City Council spokesman Eric Koch said the chamber would review the board’s decision. De Blasio spokesman Eric Phillips would not say whether the mayor supports the groups’ proposals, but said de Blasio “supports disclosure as a policy.”

“He looks forward to continuing the work to help get big money out of politics,” Phillips said.