1099-R from different state, do I need to file nonresident state taxes?

I live and work in state A. However, when I left my previous job, they sent me a check and 1099-R for the retirement I had accrued while working there, but the 1099-R is from state B.

 

My question is, even though the taxes for the 1099-R were taken out of my federal refund, do I still need to file state taxes with state B?