Creepy contractors are doing a thriving business with the city, despite being flagged by investigators for their shady — often illegal — conduct.

Among the companies that reaped millions is a Staten Island elevator-repair company used by city schools that employed a convicted child molester, a Brooklyn car wash where a worker stole a cop’s badge from a patrol car, and a Bronx security firm whose owner is a burglar.

The Mayor’s Office of Contracts requires all companies seeking to do business with the city to fill out a detailed questionnaire disclosing any past criminal or legal activity.

If a firm or its executives or employees are later found out to have been convicted of a crime or any other serious wrongdoing they are placed on a “caution list” and can be banned or suspended — or, it turns out, continue working for the city.

They include:

* Action Elevator. A probe found that the firm had an employee on the state’s Sex Offender Registry. Still, the Department of Education has shelled out over $5.6 million to the repair company over the last four years and a combined $2 million in contracts with the NYPD, Correction and Parks departments.

* The Golden Touch Car Wash in Park Slope. It was flagged after a worker got caught stealing an official NYPD shield while cleaning a police car.

* Tristar Patrol Service. The Bronx-based security firm made more than $12 million in city contracts since 2005 — despite one of its owners, Richard Zimmer, being convicted in April 1996 of attempted burglary and sentenced to five years’ probation.

Additional reporting by Joseph Goldstein