Deductions & credits

What state?  What do you mean they both can't be claimed?  Claimed as what?  Claimed as income or a deduction?  Make sure you enter the military 1099R and her SSA-1099 under the right name.   Maybe you entered both under your name or her name.   

What code is in box 7 on your military 1099R?

 

Most states don't tax Social Security.  So any taxable amount is subtracted from the federal AGI.   For Federal......

Up to 85% of Social Security becomes taxable when all your other income plus 1/2 your social security, reaches:

Married Filing Jointly: $32,000

Single or head of household: $25,000

Married Filing Separately: 0