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A Bronx principal collected thousands of dollars in overtime pay for time when she was not at work, according to city investigators who trailed her to her house and a strip mall in New Jersey to document the theft.

Liza Cruz Diaz, the principal of P.S. 31 since 2006, also used school funds to pay for Mardi Gras beads and metallic sunglasses for her daughter’s “Sweet Sixteen” party, according to a report released today by Special Commissioner of Investigation Richard Condon. The city is moving to fire her.

Cruz Diaz racked up hundreds of overtime hours by asking a secretary to punch her timecard long after she left each day. On one day that investigators trailed her to New Jersey, she left the school before 4 p.m. but wasn’t punched out until 6:21 p.m.

She also used the school’s budget to make personal purchases and falsified evidence that she had reimbursed the funds; signed her own timesheets, in violation of Department of Education policy; and smuggled records out of the building once it was clear that an investigation was underway, according to the report.

Altogether, investigators documented 111 hours when Cruz Diaz was being paid but was not working. Since 2008, she had billed 900 hours of overtime work and grossed $40,000 for it — a tally that other principals have told me borders on irresponsible at a time of budget cuts, even if the work is legitimate.

P.S. 31 is a struggling school in one of the city’s lowest-performing districts, District 7 in the South Bronx. In the last two years, citywide cuts and a hundred-student enrollment drop slashed the school’s budget by $1.2 million, to $5.9 million this year, according to DOE data. In 2010, the school lost $400,000 but increased its overtime spending by $50,000, to $210,000. This year — when the investigation was underway — that budget line dropped to $62,000.

The report paints a picture of brazen violation of city policies and an atmosphere in which misappropriating school funds was relatively simple. It also conjures one of the strangest images I’ve found in an SCI report, of an investigator earnestly taking notes on the offerings of a company that sells novelty goods (see page two).

Department officials said they would move to fire Cruz Diaz, who earns $139,000 and has worked in the system since 1989. They also said they would discipline the secretary who helped her falsify timecards.