You should divide your expenses based on who paid them; if they are deducted form a joint account, divide them evenly.

You don't have to indicate you co-own the home.

The only rule for Married Filing Separately not in a community property state is that if one spouse itemizes the other has to itemize also and the total of their itemized deductions cannot exceed what they actually paid. So, if you are not in a community property state, you may elect to split the deductions any way you would like, 50/50, 75/25, just not 100/100.

Please refer to the link below for more details:

https://www.irs.gov/Help-&-Resources/Tools-&-FAQs/FAQs-for-Individuals/Frequently-Asked-Tax-Question...

Note: Unless you have a specific reason for filing separately, joint filing gives you a bigger refund or less taxes due. Please refer to Is it better for a married couple to file jointly or separately? for details.