Kesha -- Dr. Luke Threatened to Kill My Dog

Kesha’s war with Dr. Luke got so heated during a recording session -- her dog almost got caught in the crossfire ... according to new legal docs.

Kesha just responded to her ex-producer's lawsuit against her in NY State -- and the docs lay out even more nasty allegations ... including the incident with her pooch.

Kesha says Luke threatened to put the dog down if it came near him while they were in a recording studio -- and also went after her family ... saying he'd yank her mom (and songwriting partner) off song credits.

The docs get very personal when Kesha says Luke tried to blackmail his wife into having an abortion -- and spoke openly about cheating on her.

Kesha thinks he told her all this so she'd be cool with it if he tried to cheat with her.