Pet & Dog Policy:
From the park's Frequently Asked Questions:
Can I bring my dog to the park?
Yes, but we don’t recommend it. It may sound like a good idea to take your pet to a national park but there is little you can do with them while you are here. Pets must always by on a leash or confined. They may not be left unattended in the campgrounds. They must remain on roads or in developed areas, so no hiking with them on trails or cross country. The good news is you can walk them (on leash, of course) on backcountry roads. Interesting ones to try are Twenty Mule Team Canyon Road and Titus Canyon Road into the narrows.