In den USA gibt es be-/vereidigte Polizeihunde. Entweder schwört der Hundeführer für den Hund, oder in manchen Staaten kann der Hund selber den Eid durch Bellen leisten.
Slate reports that sworn police dogs exist in the USA. It investigated the procedure of swearing (with many links).
Canine swearing-in ceremonies, on the other hand, tend to be public events celebrating the role of police dogs. In some cases, the police chief administers the human oath of office to the dog, and the handler affirms on the dog’s behalf. In rare instances, the dog is trained to bark in affirmation of the oath. When the ceremony is complete, the dog is presented with a badge to wear on its collar.
I notice some of the articles linked refer to ‘affirming’, so I suppose no Bible or other religious tome is used.