There are two instances I recall in Detective-Conan. Well one was just pointed-out now a-bit, but the first’d be in the Karaoke-Bar case. Ran & Sonoko sing a song at the some-what beginning of the episode and the song is the (I think) 2nd opening. I’m not sure what they sang in the manga though. The other is the Two-Mix episode where the case involves his seiyuu’s duo. In the manga they sang the ending of Gundam Endless-Waltz (sang by Two-Mix too), but here they sing another another song from them instead. Gundam copy-right problems? I don’t know. Also earlier in the episodes he sang the first opening.
Also random, but still kind-of relevant, listen closely to the back-ground music at 01:04 (which I assume is supposed to be played in-universe, like music for an event/gathering). I think that’s from the OST. vid. is unlisted, so if they don’t want that they can tell me and I’ll take it off from here.