Yes, as everyone else said, the head of the tick may still be embedded. Generally, if it is a dark brown/black color, it may be a deer tick, which often carry serious diseases. A light brown, leathery looking tick is typically a dog tick, which are not known as disease carriers.
Boo had a dog tick on her back last Novemeber. We filled a shot glass with rubbing alcohol, and held that over the tick until it drowned. Then, we were able to gently remove the head and body using tweezers. Pulling or cutting a tick off often causes the head to break off, and blood to spill. Also, as long as the head remains embedded in the dog, it can cause innflammation, plus it can continue to spread diseases throughout the dog's system.