Even though any changes you make to amend your federal return will automatically transfer over to your state return, you should be able to select to e-file your amended federal return only.
Most states do not allow you to e-file an amended state return, therefore, if you are provided mail-in instructions for the state return, you can disregard them. To help determine if your state allows e-file, please see this help article: Can I e-file my amended state return?