To make a long story short, I wrote a letter to my district senator and referred to him as a "local representative." I did not mean to suggest that he is a member of the state House of Representatives, but rather just a representative of my district. Is my use of the term "representative" appropriate in reference to a Senator?
If you were asking for feedback on a letter you were thinking about sending, I would suggest that this is a confusing word choice in that context. True of course, a state senator is the political representative of his state senate district. But it's confusing in that there is someone else who has a better claim to being your representative in the state legislature. Someone would have to look at it twice. Is that a small r? Oh, I guess that's correct.
That said, since you've already sent the letter, I don't find it inappropriate as such. It's more in the nature of a word choice that could have been better than one that was wrong. It is an accurate choice, but one that might require thinking to recognize as accurate.