Not all pets are at direct risk when there is a skunk on the property, so it depends on what type of pet you have. Skunks, due to their size, are unlikely to attack a cat or a dog as they could easily be killed in the encounter. Smaller animals however such as chickens, which are a less common household pet, could be in danger.
The only time a skunk is a threat to common pets such as a dog or a cat is if it feels threatened. If the dog or cat traps or corners the skunk it will raise its tail as a sign of warning before spraying the pet with its scent. This is a defense reaction and is only done when the skunk fears for its life, it aims to stun the predator while it flees. If your pet has been sprayed by a skunk it should be taken to the vet to have its eyes rinsed and cleaned and the scent removed. If for any reason you have any concerns that a skunk has bitten or scratched your pet, you should take it to the vet immediately.