The city paid nearly a quarter of a million dollars to private inspectors this spring for a “safety sweep” of the city’s tower cranes that ended days before the installation of a crane that collapsed last week and killed two people.

The private inspectors were paid $235,000 for assisting the Buildings Department’s understaffed crane inspection unit during the sweep — which lasted less than a month — after a fatal crane collapse in March killed seven people.

The crane that collapsed last Friday on East 91st Street was reportedly installed four days after the sweep ended, after the private company, McLaren Engineering, and the Department of Buildings had found eight cranes out of 30 in the city to be unsafe or lacking proper documents.

The private engineers from McLaren were hired to follow along with the publicly employed buildings inspectors to conduct “visual inspections and perform plumb and torque reports of tower cranes,” a Buildings Department official said.

The president of the New York Building Trades Employers Association, Louis Coletti, said the private inspectors had “a higher level of expertise than the average buildings inspector is able to bring to the table.”

“One of the issues that we’re struggling with is the fact that the inspectors in the buildings department are undertrained and underpaid,” he added.

A spokeswoman for the buildings department, Kate Lindquist, said in an e-mailed statement that “in light of the incident on March 15, Building Inspectors are working to complete an FDNY rigging training course and a crane safety course with the Crane Institute of America.”

She added: “We are also gearing up for Buildings Inspectors to take 32-hour certification courses on tower crane and mobile crane safety in June.”

McLaren began its contract March 29, according to the official. While the contract lasts for one year, the sweep ended April 15.

Another private company, ARXCIS, is currently working with the Buildings Department on a sweep of more than 200 mobile cranes around the city. That contract is costing the city $115,000. It began April 14. The company was due to finish by the end of May, but Buildings officials said the sweep had not yet been completed as of yesterday.

The private firms were paid on a “time and materials basis” for the inspection work, according to the official. The joint private and public inspector teams spent about four hours examining each of the 30 tower cranes.

McLaren, a West Nyack-based design and construction inspection firm, declined to comment for this story.

Myron Lee, the owner of ARXCIS, a firm based in Washington state that focuses on construction safety inspections, said he could not comment on his work with the Buildings Department because the contract stipulated that he cannot speak with reporters unless given written permission by the department.