You do. The laws vary by state. There is a statute in Missouri that dates back to the 1800s but was strengthened about 30 years ago. It allows one to kill any dog that is 'worrying livestock'.Do you have the right to protect your property ?(=to kill any dog that enter your land and kill/Threatening to kill your farm animals?)
There is also a provision that requires counties to maintain a fund to reimburse for livestock killed if the owner of the offending dogs can't be located.
That money is funded by dog licenses.
To claim reimbursement, one needs to apply within 3 days and the attack must be witnessed by another adult that is not a family member.