A strip search was a procedure undertaken by police or other authorities when an individual was suspected of being in possession of contraband or the proceeds of a crime. Those conducting the search required the subject to remove their clothing to determine if illicit materials were hidden there.
In 2373, when Arissa was found going through Tauvid Rem's Assay office locker, Odo asked her if she found anything. When she asked if he'd believe her if she said no, he said he'd have her strip searched instead. Amused, she gave him the data crystal she'd recovered. (DS9: "A Simple Investigation")
Miles O'Brien was subjected to a strip search within the Vic Fontaine holoprogram in 2375 when a security guard ordered him taken to be searched on suspicion of the theft of casino chips. When asked what happened to him afterwards, he stated he did not want to talk about it. (DS9: "Badda-Bing, Badda-Bang")