Have you actually seen her smoking on her route?
I, personally, have NEVER seen a mail carrier smoking. In my area, both at home and the businesses I have worked at, most of the mail carriers walk a large part of their route.
I don't give a fig if they are smokers, I'm just saying that I've never seen a mail carrier walking and smoking. I would find it odd if I ever did.
I wouldn't accuse her or file a complaint without absolute proof. I mean, if she is the one doing it, have something to back up your complaint so there can be no denying it on her part.
You need to find a way to be home when she's not there or whatever. Be across the street at a neighbor's house with your video camera....something. You haven't personally witnessed it, that's the thing.
You could have somebody from a few blocks away who walks and smokes and throws butts in your yard, you never know.
You need some proof is all I'm saying.
We had the bitchiest mail carrier where I work now. OMG. We kept getting mail that wasn't even the right street let alone number and she would get PISSED if we mentioned it.
She came in one day on a payday and we offered her a cup of coffee to go and some cookies. We always have those things out in the front office on payday for our employees.
She has been so nice ever since. And, we don't get the wrong mail anymore.
At any rate, my first thought is you need to find out for sure if it's her or not and then go from there.
Best wishes.