I'm very sorry for the loss of your pet. Unfortunately, there really isn't anything that you can do legally under these circumstances. Even if your pet was shot without cause, which will always be a "he said/she said" argument between you and the police who were actually at the scene, animals are considered property under Indiana law and are therefore only worth their actual monetary value. Again, I'm very sorry, this must be heartbreaking. Good luck to you.
Incidents involving dogs shot by police are increasingly common. However, absent eye-witness reports that the dog was not doing any of the acts the police claim he was, you have no basis to challenge their actions.
The foregoing is for general information purposes and does not establish an attorney-client relationship.