Yes All state parks do allow dogs and other pets in the state park and campground areas.
But all dogs and other pets must remain on a leash and are not allowed to run free during the time in the state parks.
You must also never leave the dog or other pet unattended or unsupervised and may also upon request provide Proof of rabies shots and a physical description of the dog or pet.
So make sure the dog or pet has had it's rabies shots prior to taking the dog or pet to the state park and also some areas of the parks such as picnic areas, swimming areas and food service areas may have a restriction on dogs and other pets coming into the area.