Can I sue?

[KingCon]

Ok, I know I can sue, the question is" Do I have a case?

Scenerio--I am a mailman. A woman had her box blocked and I couldnt get to it, so I drove on by, she stopped me 2 houses later and I explained to her why I didnt deliver her mail etc. She gets pissed and wants my name, I tell her " I dont give out my name, but I will give her my supervisors name/number". Then out of the blue she says' Im going to call the postmaster, because it smells like you ahve been drinking.

Well, she calls the postmaster, and my supervisor and tells them, that I was drunk, she also says she is calling the local paper. The supervisor has to come out on my route and investigate me and my vehicle looking for alcohol. needless to say, nothing was found. Anyway, everyone at work now knows about these false allegations

Do I have any legal recourse against the lady who amde the false statements?