Curtis said last week that city officials expect the search for a new chief to take several months.
When previous police chief John King resigned last week, city officials initially said he was stepping down to move out of state to care for his ailing mother. On Thursday, however, Curtis said he asked for King's resignation due to sexual-misconduct allegations.
The mayor has not detailed the allegations, beyond saying he received a report from a woman who was not a city employee on Feb. 8. He alerted the Utah County Attorney's Office to the allegations, and it passed the investigation on to the Unified Police Department and the Salt Lake District Attorney's Office to avoid any conflict.
Salt Lake County prosecutors declared in a March 1 letter to the Utah County Attorney's Office that King would not be criminally charged, citing insufficient evidence.
King had been on a short leave of absence to be with his family on the East Coast about the time the allegations were made, according to city officials. Once the investigation began, the mayor called King and asked him to extend his leave.
After city officials learned the chief would not be charged, he was taken off administrative leave.
But later, more details of the investigation were made available to Curtis, city officials said, and the mayor was "uncomfortable" with those details which sparked their mutual decision that King resign.
Curtis said last week that the situation involved "deep complexities," but he would not provide any further details. Unified police officials and Salt Lake County prosecutors also have declined to release more information.