animal control should investigate any and all reports of neglect no matter what the species involved. by law they have to i think.
anyhow, for your info what they'll always do is investigate the report, talk to the owner and give them a deadline to get the animal checked out by a vet. they will follow through with the owner to make sure they're complying with their demands. if the owner does as they're told most times they'll get a few more follow up visits before the case is closed out. if the demands are not met then i think thats when they start going
"ok you can either sign this animal over to us or we can get a warrant and seize it."
if the animals condition is considered life threatening when they come out to make the initial investigation, i think thats when they automatically go to removing the animal from the owner's possession.
but usually they always try the "educate the owner on that animals care" approach.