Police in Springfield, OH tell TMZ ... the department is getting double the amount of daily calls -- which was already in the hundreds! -- from concerned citizens across the country, all asking the same thing ... are immigrants really eating people's pets?!?

Cops say the increased call volume started after Trump pushed the debunked conspiracy about Haitians in Tuesday night's debate against Kamala Harris ... when he said immigrants were eating cats and dogs in the city, which he called out specifically.

Springfield Police say there have been ZERO reports of animal killings and consumption ... but that's not stopping folks from inundating the PD with calls seeking info on Trump's conspiracy theory.

We're told the non-stop barrage of calls is taking officers' time away from real police work on other cases ... and it's safe to say they are over the nonsense!

As we reported ... there has been one instance in Ohio of a woman allegedly killing and eating a cat ... but the woman arrested in the case is a U.S. native -- born and raised in Ohio -- and the alleged incident happened in Canton, not Springfield.

Trump was fact-checked by moderator David Muir during the debate on ABC, with Muir citing a Springfield city manager who said no pets had been harmed in the city.

Donald Trump Jr. later shared a 911 audio recording of an Ohio caller claiming they saw 4 Haitian migrants carrying dead geese, presenting the call as supposed evidence of his dad's claims ... and he later posted the police report from the apparent incident as well.