Does each Form 1099-R show a gross distribution of the total of all of the monthly distributions or does each one show half of the annual total? While the payer might have shown half of the annual total (6 months) on separate Forms 1099-R and the entire amount on each reported as taxable in only one state, a Form 1099-R has two lines for boxes 12, 13 and 14, allowing each state's portion of the annual total to be reported on a single Form 1099-R.
If each Form 1099-R shows a a gross distribution of the entire annual amount, contact the payer for corrections.
Taken at face value, both Forms 1099-R need to be reported and the sum of the two will appear as income on your federal tax return. It appears that you'll have to file part-year resident tax returns for both states.
