Can one co-owner claim CCA on a rental property while the other doesn't?

Yes. CCA is claimed separately by each co-owner on their own proportionate share of the property's undepreciated capital cost, so it's an individual choice for each owner, not something that has to be claimed uniformly by everyone who owns the property together. One co-owner can choose to claim CCA on their share in a given year while the other decides not to, based on each person's own tax situation.

This makes sense once you remember that CCA is optional in general - nobody is required to claim the maximum CCA available in any year, and each taxpayer decides for themselves whether it makes sense given their overall income and tax position that year. A co-owner might choose to skip a CCA claim because their rental income is already low that year, remembering CCA can't create a rental loss, or because they're planning ahead for a future sale and want to preserve UCC. Each co-owner keeps track of their own UCC balance independently going forward, so one person's decision to claim or not claim CCA in a given year doesn't affect the other co-owner's own UCC pool or future options.