Moved to another state at end of year. Do I put my old address or new address on my Fed and State returns?

I closed on sale of old home Jan 4.  But left the house Dec 29.  Purchased new home in new State Jan 16.  I'm due a refund from old state but if I put my old address I may not receive the check. Could get lost in mail even though I have forwarded mail.  Which address should I use on my Form 1040 and State Returns?

Please advise