If you don't mean " Would you like to stay", then it depends on the tense : choose yours :P
Which room do you stay in madam ? (simple Present)
are you staying (Present continuous)
have you stayed (Present perfect)
have you been staying (Present perfect continuous)
Which room did you stay in madam ? (simple past)
were you staying (past continuous)
had you stayed (past perfect)
had you been staying (past perfect continuous)
Which room will you stay in madam ?(simple future)
will you be staying (future continuous)
will you have stayed (future perfect)
will you have been staying (future perfect continuous)
Which room would you stay in madam ?(simple conditional)
would you be staying (conditional continuous)
would you have stayed (conditional perfect)
would you have been staying (conditional perfect continuous)
NOTE : Some of these tenses would need some more words in the sentence to make them complete :)
e.g. Which room would you have stayed in madam, if I had told you that room number 103 has a treasure chest hidden in it ? :D