I don't believe so. There's a sign at 0.0 mile marker off S.R. 605 Bloomsbury Road. It lists rules. No permit is mentioned. They just don't want you going down the private driveways which cross the Trail.
No longer required - it became a quasi public trail awhile back - notice was in the local post. There is also a website that can only seemingly be found through the Facebook page that has more current information than the 'Friends' website. http://www.dahlgrentrail.org/ It's a rough ride and the only facilities are at the Sheetz at the end.
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