Comptroller William Thompson Jr. is launching an audit of the Bloomberg administration’s efforts to lower class sizes, following a report arguing that more than $150 million in state money targeted at class-size reduction has brought only minimal improvements and even some backsliding.

Released yesterday, the report commissioned by the city teachers union for a fee of $6,000 studied a group of schools that said they planned to use a new pot of state dollars to reduce class sizes. It found that only half actually accomplished the goal, while about a third actually increased class sizes.

The money was handed out by the state as part of an effort to settle the years-long Campaign for Fiscal Equity lawsuit, which recommended targeting an increase in funding for city schools to specific goals, including class size reduction.

The Bloomberg administration’s Department of Education has repeatedly dismissed class-size reduction as a priority, but under pressure from the state Education Department officials wrote out a plan promising to “coach” certain target schools and to devote a large portion of the new funds — $153 million of $258 million total — to class-size reduction.

A Department of Education spokesman, David Cantor, yesterday said the UFT-backed report was “factually flawed” and that class sizes have dropped at “virtually every grade level since 2002.”

In the past, the department has touted reductions by referring to citywide averages, which the union and its allies yesterday said mask many schools where class sizes are going up.