For expenses paid before the divorce, you can can divide them in any way that you agree is reasonable.  Usually that means whoever actually paid each bill.  Or split it 50/50 or 60/40 if one persons income is higher.  Specific  personal deductions like tuition, state income tax and medical expenses would be claimed by the specific person.  

You just don't want to over-claim anything because if the IRS audits you, then they get to decide.