New Revised Standard Version
an oath before the LORD shall decide between the two of them that the one has not laid hands on the property of the other; the owner shall accept the oath, and no restitution shall be made.

Contemporary English Version
If you swear with me as your witness that you did not harm the animal, you do not have to replace it. Your word is enough.

New American Bible
there shall be an oath before the LORD between the two of them that the guardian did not lay hands on his neighbor’s property; the owner must accept the oath, and no restitution is to be made.

Douay-Rheims Bible
There shall be an oath between them, that he did not put forth his hand to his neighbour's goods: and the owner shall accept of the oath, and he shall not be compelled to make restitution.

There shall be an oath between them, that he did not put forth his hand to his neighbour's goods: and the owner shall accept of the oath, and he shall not be compelled to make restitution.

an oath of the Lord

Leviticus 5:1 If any one sin, and hear the voice of one swearing, and is a witness either because he himself hath seen, or is privy to it: if he do not utter it, he shall bear his iniquity.

Leviticus 6:3 Or shall find a thing lost, and denying it, shall also swear falsely, or shall do any other of the many things, wherein men are wont to sin:

1 Kings 2:42,43 And sending he called for him, and said to him: Did I not protest to thee by the Lord, and tell thee before: On what day soever thou shalt go out and walk abroad any where, know that thou shalt die? And thou answeredst me: The word that I have heard is good. . . .

Proverbs 30:9 Lest perhaps being filled, I should be tempted to deny, and say: Who is the Lord? or being compelled by poverty, I should steal, and forswear the name of my God.

Hebrews 6:16 For men swear by one greater than themselves: and an oath for confirmation is the end of all their controversy.

that he hath not

Exodus 22:8 If the thief be not known, the master of the house shall be brought to the gods, and shall swear that he did not lay his hand upon his neighbour's goods,

Exodus 23:1 Thou shalt not receive the voice of a lie: neither shalt thou join thy hand to bear false witness for a wicked person.