Citizen repeatedly calls animal control about the condition of a neighbor's dog. Calls go through police dispatch, and an officer is often dispatched WITH animal control, but does not go alone.

Dog is fine. Calls are an attempt to get neighbor in trouble.

False report doesn't seem to fit, as animal control is not law enforcement. Thoughts? Ideas?

Maybe 38.15(a)(6)? But, subsection (d) must be taken into account.

May also be impairing the verity of a governmental record under 36.10(a)(3), or that may be a way to argue something more than speech only is involved?

Next time the neighbor calls, send a police officer to take a report in person from the neighbor.

maybe 42.07 (4) harassment? or possibly 42.06 false report