The tax payer who claims the rental income, is the one who claims the expenses, to include the property taxes.
Typically, for a married couple to file separate returns means that they pay more in taxes overall. But that's the taxpayer's call.
If both of you own the rental, you can each claim 50% ownership and split all income/expenses right down the middle on your separate returns.
When a married couple files separate, they both automatically disqualify for deductions they would otherwise qualify for if they filed joint. One thing affected (of many) is the EITC, as well as education credits. Also, when filing separate if one of you itemizes deductions, then the other is required to also itemize deductions, even if the itemized deductions of one of you are zero. Likewise, if one takes the standard deduction, then both must take the standard deduction even if the itemized deductions of one of you would be higher.
