The spouse who "Contributed to" (purchased) the RRSP 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 contributors RRSP limit defining how much can be purchased and the purchaser also claiming the deduction on their tax return.
If you only have one slip, you only make one entry in TurboTax to the spouse's tax return who "contributed" to the RRSP. The Annuitant will see no tax consequences untils funds are withdrawn from that Spousal RRSP.