If it says "search", you MAY search and not find. If it says "choose", you MUST choose if there is a legal choice.
Slight nitpick: If you have to "search" for a card with a certain quality (such as instant, or red, or basic land), you may opt to not find one. If you have to "search" for any card, however, you must find one.
Further nitpick: if a card says "search for any card" you don't have to find one if there are no cards to find. Like Demonic Tutoring on an empty library.
If that seems like a pointless ruling to have, let me say that it's probably there for Magic Online, cause something like that can really fuck a computer up.