Just Kill a Heifer and it will be ok

Deuteronomy 21:1 says,  "If one be found slain in the land which the LORD thy God giveth thee to possess it, lying in the field, and it be not known who hath slain him:  21:2 Then thy elders and thy judges shall come forth, and they shall measure unto the cities which are round about him that is slain:  21:3 And it shall be, that the city which is next unto the slain man, even the elders of that city shall take an heifer, which hath not been wrought with, and which hath not drawn in the yoke;  21:4 And the elders of that city shall bring down the heifer unto a rough valley, which is neither eared nor sown, and shall strike off the heifer's neck there in the valley:  21:5 And the priests the sons of Levi shall come near; for them the LORD thy God hath chosen to minister unto him, and to bless in the name of the LORD; and by their word shall every controversy and every stroke be tried:  21:6 And all the elders of that city, that are next unto the slain man, shall wash their hands over the heifer that is beheaded in the valley:  21:7 And they shall answer and say, Our hands have not shed this blood, neither have our eyes seen it."  Umm... What did the heifer do?  Why does God insist on killing innocent animals.  what does this prove?  The elders wash their hands over it.  Couldn't they have left the animal alive for that?  And since when does a corpses proximity to a city prove that the guilty person lies in the city?  Shouldn't they investigate the crime and leave the poor innocent heifer alone?