The Chicago Public Schools’ facilities chief — one of schools CEO Forrest Claypool’s hires from the city agency he formerly headed — has resigned from his $165,000 post amid residency questions.

Jason R. Kierna, 30, has headed Claypool’s lead testing and mitigation efforts in schools, and also has been involved in the ongoing move to privatize the management of all school buildings.

Kierna, who gave notice Wednesday, did not return messages seeking comment. His last day on the job will be Friday, Feb. 3.

Since February 2015, he and his wife have owned a home in La Grange Park. He was allowed to live there, rather than in the city, at his previous job, with the Chicago Transit Authority, where he also worked for Claypool. But he was supposed to move to the city within six months of being hired by CPS in January 2016, under the school system’s residency requirement.

His current driver’s license and car registration and his wife’s driver’s license show two North Side addresses where they formerly lived. His wife’s current car registration shows the La Grange Park address. That’s also the address where the couple’s property-tax bill is mailed.

Kierna pays $800 a month for an apartment on the Far Northwest Side, according to a lease and copies of rent checks provided by a CPS spokeswoman, though his family has remained in La Grange Park.

The Chicago Board of Education at times has approved “special needs” waivers of the residency rule, but Kierna didn’t apply for one.

In August 2015, it gave a two-year waiver to Ronald DeNard, Claypool’s $225,000-a-year senior vice president of finance, who owns a home in Flossmoor. That came over the objection of Inspector General Nicholas Schuler, who said the residency waiver might raise concerns “of preferential treatment for favored insiders.”

“As it has done in the past, the Board of Education can grant a waiver for a limited period of time to allow a candidate from outside Chicago to begin working for the district,“ a district spokesman said at the time.

According to CPS’ residency policy: “The question of an employee’s residence is principally one of where employee intends to live and have his or her one true, permanent home or domicile to which an employee intends to return following an absence. In disputed cases, the burden of proof rests with the employee.”

The policy says determining residency “shall consider, but not be limited to, the following factors: voter registration, place of filing tax returns, property ownership, driver’s license and car registration.”

CPS has recently toughened its policy for students found to have falsified home addresses to gain an advantage in selective-school admission, banning them for life from all test-in schools.

In December, Schuler’s office put out a report detailing cases of students booted out of schools and staffers fired and tagged with a “do not hire” designation that will prevent them from returning to work for CPS.

One case targeted a Highland Park family who rented a studio apartment in Rogers Park so their two kids could go to Northside College Prep. Another involved a Berwyn family whose daughter attended the popular Andrew Jackson Elementary School — and said they were renting an apartment in in a Chicago building belonging to a family member in time for their son to apply to selective high schools. All of these children were removed from CPS schools and both families hit with five-digit tuition bills. CPS also sent word of the Berwyn parents’ residency issue to their employer, the City Colleges of Chicago, which, like the public schools system, requires workers to live in the city.