According to Weston Pediatric Physicians, there is no additional danger if a tick is removed but the head remains in the skin. The head eventually falls out or falls apart without intervention. Any infections that pass from ticks to animals or humans are located in ticks' stomachs.
WebMD recommends pulling the tick out by gripping it where it touches the skin of the animal or person. Tweezers or tick-removal devices both work well. The parasite should be pulled out gently without twisting its body. The tick should be bagged and frozen in case an infection develops. The area of the bite should be washed thoroughly with soap and water.