Curtis, a Republican who has opposed gay rights legislation, had claimed he was the victim of an extortion scheme, but that contention led to disclosure of details about his alleged sexual behavior, The (Vancouver, Wash.) Columbian reported.
Spokane police said Curtis met Cody Castagna, 26, at a porn store and subsequently had sex with him in a hotel room. Castagna said he was promised $1,000 to have unprotected sex with Curtis, and had to press Curtis for payment.
An attorney for Castagna told NBC News he is concerned his client could face charges. KXLY-TV in Spokane reported prosecutors were considering whether to charge Curtis with solicitation.
"Today, I submitted my letter of resignation to Gov. (Chris) Gregoire, effective immediately," Curtis said in a letter released by the Republican caucus.
Curtis, a retired fire captain, said the scandal "has been damaging to my family, and I don't want to subject them to any additional pain that might result from carrying out this matter under the scrutiny that comes with holding public office."