If you Efile your Federal and State Returns, then download or print a PDF copy of your returns, you will have a page of Filing Instructions for both your Federal and State returns.
If your State Filing Instructions instructs you to to mail a copy of your 1099-R, details about where to send it will be given.
However, this would be rare if you are Efiling your State Return. If you entered your 1099-R in your Federal return, it would be included in your state return also.