The policy is for caches, but the guidelines for letterboxes should be the same. They are permitted in the park but must follow guidelines (see link below):

Promotional page:
http://www.arkansasstateparks.com/things-to-do/geocaching/

Policy:
http://www.arkansasstateparks.com/images/pdfs/geocaching/geo-policy.pdf

Permit:
http://www.arkansasstateparks.com/images/pdfs/geocaching/geo-permit.pdf