Bounty hunters are not allowed to kill anyone unless it is in self-defense.  Bounty hunters have the same rights as civilians when it comes to self-defense. For a bigger list see this article on what bounty hunters are legally allowed to do.

Bounty Hunters Sued The Family For Shooting Them

In a Texas case, bounty hunters Richard James and his partner DG Pearson were arrested in 2001 for felony charges during an arrest. The charges were levied by the fugitive and his family but were later dismissed against the hunters after the fugitive’s wife shot a deputy sheriff in another arrest attempt of the fugitive by the county sheriff’s department. The hunters sued the fugitive and family, winning the civil suit for malicious prosecution with a judgment amount of $1.5 million. Link.