As the pilot - you should know whether you are RVSM approved/equipped/able. If you don't know what chance have we got?
When we get strips produced on your flight there are attention getters printed to highlight those which we are unsure of or have been told by the operators that they are not RVSM compliant. If you were given FL320, no questions asked, your operator must have confirmed that you are RSVM compliant.
If you have any doubts, tell us and normal separation can be applied - it's your lives and our licences!