The warrant indicates state police contacted a handful of workers who admitted to falsifying registrations.
Marion County Prosecutor Terry Curry said he had spoken with State Police and asked the agency to comment no further on the investigation.
Indiana State Police says voter suppression and civil rights violation allegations against the department are completely false.
Police say the animal either fell or was thrown from a moving vehicle. The alligator died before animal control workers arrived.
Indianapolis is one of only six cities singled out for national recognition.
The ISP is hoping new pickup trucks will let troopers see how motorists drive when they think no one is watching.