India -- the ex-"Celebrity Big Brother" contestant who's a transgender woman -- spoke to Byline TV regarding the issue ... claiming she's gotten Northumbria Police involved, as she says J.K. has consistently referred to her as a man despite her legal status as a woman.

She says J.K.'s alleged repeated misgendering constitutes a crime in the U.K. -- suggesting it violates the Equalities Act and Gender Recognition Act. India also hints this could possibly qualify as a hate crime ... but at the very least, thinks it's a malicious communications case.

Variety reports that Northumbria Police are on standby, ready to have a chat with the author about this whole ordeal ... but no word on whether J.K.'s gonna play ball.

Meanwhile, J.K.'s already fired back ... saying she's already consulted a lawyer who not only reckons she has a solid case against IW for defamation, but says India constantly targeting J.K. online might qualify as harassment -- so she's mulling legal action of her own.

J.K. adds, "Aware as I am that it's an offense to lie to law enforcement, I'll simply have to explain to the police that, in my view, India is a classic example of the male narcissist who lives in a state of perpetual rage that he can't compel women to take him at his own valuation."

Of course, Rowling's faced a ton of backlash for her controversial remarks about transgender folks. She's been called out as a "TERF" (trans-exclusionary radical feminist) and labeled a bigot by many -- some of the 'HP' cast have even distanced themselves from her.