Ending the game in Bughouse

When playing Bughouse, suppose one board is in a position where the king is checkmated, if this were normal Chess.  However, it would be possible to interpose a piece.  No pieces on your board are available to intermpose.  Can you "drop" a piece onto the space, saving yourself from checkmate?

What if you have no pieces available for dropping?  Can you wait until your partner gives you one?

I know that answers may vary depending on local rules, but when played by whatever passes for "official" rules in America, what happens?  The closest thing I know to a definitive set of official rules would be the rules used at the Bughouse tournaments held at the junior national championships hosted by USCF.