Mountain beavers appear relatively free of diseases and internal parasites. Animals in western Washington were checked as possible carriers of plague but were found negative. A large flea (Hystrichopsylla schefferi) unique to mountain beavers is common on the animals but is not known to be a problem for humans. Mites (Acarina spp.) often infest the ear and eye region.
Nevertheless, always avoid contact with wildlife whenever possible to reduce risk.
Resources: (online)
Mountain Beavers