Some areas of national parks dogs are allowed while some other parts of national parks dogs are prohibited.
If dogs or other pets are not allowed in those areas of the national park there will be signs posted about the prohibition of dogs or pets in those areas of the national parks.
Dogs are allowed in national parks but only in developed areas, on fully paved roads, sidewalks, along bike paths etc.
Dogs are also allowed in some campgrounds but not walk in campgrounds and you must keep the dog on a leash at all times.
The lease that you keep your dog on must be no longer than six feet in length and you must keep your dog attended to at all times.
So you cannot leave your dog unattended and tied up in the national park.