Missouri: (Revised Statutes)
273.020 In every case where sheep or other domestic animals are killed or maimed by dogs, the owner of such animals may recover against the owner or keeper of such dog or dogs the full amount of damages and the owner shall forthwith kill such dog or dogs; and for every day he shall refuse or neglect to do so, after notice, he shall pay and forfeit the sum of one dollar, and it shall be lawful for any person to kill such dog or dogs; provided, however, that whenever in any case the facts shall show that in the worrying or killing, maiming or wounding of any said sheep or other domestic animals that the same was done by two or more dogs belonging to different owners, then the plaintiff, the person whose animals were killed, wounded or maimed, may at his or her election, join all of the owners of said dogs as joint tort-feasors or may sue each one separately at his or her election.
273.030 If any person shall discover any dog or dogs in the act of killing, wounding or chasing sheep in any portion of this state, or shall discover any dog or dogs under such circumstances as to satisfactorily show that such dog or dogs has or have been recently engaged in killing or chasing sheep or other domestic animal or animals, such person is authorized to immediately pursue and kill such dog or dogs; provided, however, that such dog or dogs shall not be killed in any enclosure belonging to or being in lawful possession of the owner of such dog or dogs.
If your birds are killed one of the sources of recompense is described in this section:
273.070 1. County clerks shall issue licenses to applicants and shall deliver to the applicants a metallic plate having the number corresponding to that of the license stamped thereon and shall deliver to such party a certificate from the book furnished to him by the secretary of state, which said certificates, as well as the margin or part thereof remaining in the book after cutting out the certificate, shall contain the number of the license, the year for which the same is granted, the name and residence of the owner of the dog, and the sex, color and description of the dog for which the license is paid and the amount of the tax paid therefor.
2. Such clerk shall retain out of the money received for such license issued the sum of ten cents, which shall cover all his services under sections 273.040 to 273.180, and he shall pay the balance and all other sums received by him under the provisions of sections 273.040 to 273.180, less the cost of license tags, record books, blank applications and affidavits and the cost of transmitting the balance to the treasurer of the county.
3. The treasurer of the county shall set any and all sums so received apart in a separate fund to be known as a "County Dog License Fund", and such fund shall be used only for the purpose of compensating persons who have suffered loss or damage through injury or killing by dogs of any livestock or poultry owned by them and located in said county at the time of such injury or killing, in an amount not to exceed the market value thereof at the time of such injury or killing. The county commission of each county in this state is authorized to expend and draw county warrants against such fund only as herein provided; provided, that sections 273.040 to 273.180 shall not be construed to prevent suits at law for damages caused to livestock or poultry by dogs.
Animal Abuse and Neglect Statute: (pertinent exception)
578.009 (9) The killing of an animal by any person at any time if such animal is outside of the owned or rented property of the owner or custodian of such animal and the animal is injuring any person or farm animal but shall not include police or guard dogs while working.
Link to University of Missouri's Ag Law center:
http://aglaw.missouri.edu/