DURHAM, N.C. — A day after Gov. Pat McCrory signed a bill prohibiting so-called sanctuary city policies in North Carolina, Jose Lopez, the police chief in Durham, was assessing the effect it would have on this city, where, for the last dozen years, police officers have been instructed to limit inquiries about a person’s immigration status.

In order for Durham to comply with the new law, Chief Lopez said, the local rule would have to come off the books. Although he said he would still recommend that his officers refrain from poking their noses into immigration matters, he predicted that rumors would spread among undocumented immigrants that it was no longer safe to cooperate with the Durham police.

“That’s going to bring a distrust,” said Chief Lopez, who is of Puerto Rican descent. He was picked eight years ago to lead the police force in this old tobacco town, home to Duke University and a Hispanic population that more than doubled last decade, but will retire at the end of the year,

“It will cause individuals to flee the police, on the belief that some minor incident is going to get them deported,” he added.