I don’t know if cozys are romance novels, but I do know Stacy Abrams used to write them and she could very well be three men, maybe five.
Violence happens off screen for the most part.
Murder She Wrote would be considered a Cozy Mystery.
The four types of mystery are the police procedural (starring the police, natch!) the hard boiled detective (featuring a private eye who quite often was involved in law enforcement), the law and order (starring a lawyer) and the amateur sleuth which may or may not be a cozy.
Men tend to write more police procedural. Women tend to write more amateur sleuth. And Cozys are VERY female dominated.