Roger Mundell Jr. went into the garage in Brookfield on Sunday morning to fetch some tie-down straps for a friend when the animal attacked.
It then ran out of the garage and bit Mundell's 15-year-old nephew on the arms and back.
Mundell and his wife pinned the cat to the ground and shot it dead.
Mundell, his nephew and his wife, are being treated for rabies. His wife wasn't bitten, but got the animal's blood on her.
State Environmental Police took the bobcat to have it tested for rabies, which they think is likely given its unusual behavior.