I'm a fellow user. I don't work for TurboTax and am not a tax person. I don't know anything specific about Maryland state returns, so I can only tell you what I'm seeing.
The Form 1040X and associated forms go to the IRS. You can get the address from the table I linked to in my answer below.
The Maryland 502X (if it's a resident return) goes to the Maryland state tax agency.
On the first page of the Maryland return there are some questions (see the PDF I linked above). One of the questions is:
"Is an amended federal return being filed? If yes, submit copy."
That implies to me that the Federal and State returns can be filed at the same time, but that you also submit a copy of the amended Federal return along with your state amended return. In other words, the State wants to see your amended Federal return, too.
You shouldn't have to wait to hear back from the IRS. That can take up to 16 weeks.
