Suppose a man goes to a private residence and pays for a massage. During the massage, sexual contact takes place. After this activity, the man leaves and goes about his day. Is it possible for the man to be arrested for soliciting a prostitute days later if the police never caught him and the masseuse on the day the activity took place? The question is asked in the event that the masseuse gets busted later and shares contact information with the police.
Short answer is yes. The government can base its case on direct evidence or circumstantial evidence. So if there are reciepts that say you went there for a message that would be circumstantial evidence.
The hard part obvioulsy would be proving that it was sexual in nature. But charges cna be brought just because you weren't caught in the act.
The police need not have observed the act for a prosecutor to take up the case. Testimony of the "masseuse," if believed, is sufficient to support a conviction. See, for example, State v. Wilson, 5th Dist. No. 09-CA-4, 2010-Ohio-139 at par. 40, stating "[t]he testimony of one witness is sufficient to prove a fact." It doesn't matter whether the witness is a prostitute, a drug dealer, a pimp, or whatever else.
Also, the statute of limitations on misdemeanors is two years under R.C. 2901.13(A)(1)(b) so there's plenty of time.
Also, I'll add, this is more or less how Jerry Springer got nailed when he was Cincinnati's Mayor. A police raid uncovered a check he used to pay a prostitute.
See--Plotz, David (1998-03-22). "Jerry Springer". Slate. Retrieved 2007-06-21--
Springer was elected to the Cincinnati city council in 1971. He resigned in 1974 after admitting to hiring a prostitute. The episode was uncovered when a police raid on a Fort Wright, Kentucky "massage parlor" unearthed a check Springer had written for its "services". Springer came clean at a press conference. Long-time Cincinnati newsman Al Schottelkotte pronounced Springer's career over, but Springer's honesty helped him win back his seat in 1975 by a landslide. In a post-election interview, Schottelkotte good-naturedly reminded Springer that he had declared Springer's career over. Springer told the newsman, "I'm glad that you were wrong." In 1977, he was chosen to serve one year as mayor by the City Council.