When Natalie first meets Leonard, she does not even know that Jimmy is missing. Actually she mistakes Leonard for him and when she realizes that someone else is wearing her boyfriend's clothes and has his car, she knows something is not quite right.
When Leonard enters Natalie's bar, she takes "revenge" on him by serving him the spit cup. She then realizes that his condition is real. That's probably the reason she doesn't really suspect him of murdering her boyfriend. How could someone who can't even remember the last ten minutes kill a tough guy like Jimmy?
And even Leonard was involved, can he really be held responsible with his inability?
Jimmy was a drug dealer and as we find out later he owed some bad people money. Natalie knows that and she doesn't really know what exactly happened to him.
However from the start she never really trusts Leonard or really befriends him, she mostly just uses him for her own selfish reasons. Only in the end she is a little bit more sympathetic after he helped her get rid of her "problem".
So in conclusion I think the main reason for not Natalie not suspecting Leonard is his condition. And even if she did suspect him, for her there is not much point in revenge or going to the police. She is a very pragmatic person and rather uses him for her own advantage than caring about "justice".