"...a very good idea to have permits from both states."
If you're actually hunting that close to a state line, you'd do well at least to talk to a game warden whose area of concern is just over the line from where you hunt. Call it cheap insurance. After all, if you can trail a wounded deer, a game warden should be able to back-trail that deer to the place where he was shot.
Or, for the sake of your billfold and peace of mind if you're all that worried about this sort of truly-rare and highly-unlikely problem, be quiet and go home.
You're from BATFE? Come right in! I use all your fine products!