You can always apply for a mortgage seperately. However, the State that the property is in will factor into whether or not the non applicant spouse's debts have to be counted against the applying spouse.
If you are in a Community Property State, my understanding is that even if only one spouse is going on the mortgage, all debts from both spouses will be used to calculate the debt to income ratios. The debt to income ratios will play a role in determining how much you can afford and loan program (FHA currently allows up to 56.99% whereas Fannie Mae has a cap of 45% in most situations).
I have never originated a loan in a Community Property State, so I would do some additional checking before making any decisions.
Thanks for this info TC. We will be looking for a house in PA, a non community property. My wife's student loan is in her name so I should not include her on any mortgage applications so that my loan to debt ratio will be smaller. But we can still put her name on the title. Do I have this correct?