After a nine-month investigation, Barneys New York has agreed to pay $525,000 in costs, fees and penalties and institute a host of reforms to settle accusations that it singled out minority shoppers for heightened surveillance at its store on Madison Avenue.

Mr. Christian, in lawsuit filed against both the city and the store in State Supreme Court, said he had purchased a Salvatore Ferragamo belt with his debit card, only to be chased down and accused of stealing the item.

He was stopped several blocks from the store on Fifth Avenue by plainclothes officers who questioned his ability to pay for the $350 belt. The officers also said the debit card must have been a fake, according to the suit. Mr. Christian was handcuffed and taken to the 19th Precinct station house, where he was held, according to the suit, for about two hours before being freed.

Ms. Phillips described being “stopped, frisked, searched and detained” by the police at Barneys after she bought a handbag valued at more than $2,000.

In its agreement with the state, Barneys pledged to hire an “independent anti-profiling consultant with expertise in the prevention of racial profiling in loss prevention and asset protection.” The store also vowed to improve its record keeping, limit access to its surveillance videos and reform how it detains suspected shoplifters.