Married filing separately. House is in our name but loan is in spouse. Who claims taxes

If you are filing separately, you can Split the property taxes between the two or report the entire amount on the return that receives the most benefit. But you must make sure to not report the entire amount on both returns or the sum of a split amount that will exceed the actual reported amount.

Remember that when filing separately from your spouse, if one return uses itemized deductions, the other must as well - even if the total is less than the standard deduction.

If you live in a community property state, you may also benefit from the discussion here: 

Married Filing Separately in Community Property States