Here are some statues on animal cruelty in Louisiana. It seems to me it is the duty of the DA or police to investigate this case. it is an admitted dog beating case. https://www.animallaw.info/statute/la-cruelty-consolidated-cruelty-statutes
If the police does not investigate make an arrest and if the DA does not act they all could be breaking this statute which clearly states "failure to act" which if results in more cruelty it would be legally on their hands as well. § 102. Definitions; cruelty to animals The following words, phrases, and terms as used in R.S. 14:102.1 through R.S. 14:102.4 shall be defined and construed as follows: (1) "Cruel" means every act or failure to act whereby unjustifiable physical pain or suffering is caused or permitted.