Well, some things don't match, but I'll still try with Blue Steel:
On her first day on the job, NYPD officer Megan Turner, the lone
officer on the scene, shoots and kills the perpetrator of a
supermarket hold-up. Since no gun was found on the perpetrator's
person or at the scene and none of the witnesses could corroborate
Megan's story definitively that the perpetrator was indeed wielding a
gun, she is suspended from active duty. She is quickly albeit
temporarily reinstated to the position of homicide detective because
the spent shell casing from the bullet used in a subsequent murder had
her name carved on it. This murder ends up being only the first in a
series. Working on the case with fellow homicide detective Nick Mann,
Megan initially has no idea who in her life could be the murderer. In
short order, the murderer does show himself to her. He is commodities
trader Eugene Hunt who she met immediately following her suspension
and who she has since dated. He also implies to her that he was in the
supermarket at the time of the hold-up and that he ...
Here she is a cop (which you didn't mention, though) accidentally killing someone. But she is stalked on the phone by a guy that saw this and goes on his own killing spree. And it is later revealed (to her, we know all the time, I think) that he is the guy she was dating and after that he one time also appears at her family's house playing her "friend", while only she knows how dangerous he is.
But some points don't match. He doesn't have a limp and, being Ron Silver, he always wears a beard (though still well-presented). But maybe you have mixed him up with her partner, who is clean-shaven (and with whom she starts an affair at the end, too, I think).