The animal killed in Mexico was from the Crocodylus acutus species
The incident happened at a water treatment plant in the north-western state of Sinaloa. An investigation has been launched.
The man is facing criminal charges and up to nine years in jail, as crocodiles are a protected species in Mexico.
Local media say the crocodile posed a threat to the local population.
The footage shows the man shooting at the crocodile several times after it was pulled to the side of the pond in a fishing net.
A group of men in civil defence shirts are seen cheering.
They warn the police officer that the animal is still alive and ask him to shoot it in the head.
A second man in uniform then joins him and both men finish the crocodile off with pistols.
The mayor of the city of Ahome, where the water treatment plant is located, said there was risk to the population.
The decision to kill the crocodile ?should be analysed in the view of the danger,? Mayor Arturo Duarte Garcia told the AP news agency.
He added, however, that ?the excess of violence in this case is regrettable?.
Sinaloa is the home state of Joaquin ?Shorty? Guzman, who was Mexico?s most wanted man until his arrest in February 2014.
He was the leader of the Sinaloa drug cartel, which controlled much of the drug traffic to the US via Mexico?s Pacific coast.