If the box reads Kings Mills, Ohio, or Cincinnati, Ohio, its pre-WWII, or at least that's my understanding. I know there are some guys on this board collecting Peters and they will hopefilly chime in with more precise info.
I think Remington bought Peters in 1934 or 5. The Remington plant was in Bridgeport, CT.
Foot note on my local history
The Plant closed in 1986 and the shot tower still stands today. You can see it from I-95. If you ever want to spend a few hours looking at our manufacturing and urban history photo search Bridgeport CT and Remington
I have a passing interest in the history of that city, interesting to say the least.
Remington started moving some operations from Kings Mills to Bridgeport just before world war II. Shotgun and possibly 22 production being the last produced in the old Peter's plant. After the war they sold off the old plant (which is still standing today) but all Peters ammo was made in Bridgeport. I believe your box style was used from @ 46 till the mid 50's.