If I co-own my home with a Canadian citizen spouse, do I still have Underused Housing Tax filing obligations?

Possibly, yes, even though your spouse is a Canadian citizen. The Underused Housing Tax generally looks at each owner's individual status with respect to their own share of the property, rather than treating the whole property as automatically excluded just because one co-owner happens to be a Canadian citizen or permanent resident. If you are not yourself a Canadian citizen or permanent resident, your ownership share can still make you an affected owner with a filing obligation, regardless of your spouse's status.

Whether any tax actually ends up being owed once exemptions are considered is a separate question from whether a return needs to be filed in the first place - and because several exemptions must be actively claimed rather than applying automatically, filing can matter even if you ultimately expect to owe nothing. Joint ownership with a Canadian spouse is a common situation that catches people off guard for exactly this reason.

If you co-own residential property with a Canadian citizen or permanent resident spouse and are not one yourself, confirm your own filing obligation with a tax advisor rather than assuming your spouse's status covers you.