The spouse who "Contributed" to the RRSP (the Contributor) claims the deduction on their tax return. Your RRSP Contribution Slip should be marked with the Contributor and the Annuitant.
Spousal RRSPs are treated the same as a regular RRSP contribution when purchased, with the purchaser's RRSP limit defining how much can be purchased and the purchaser also claiming the deduction on their tax return.