If the software you are using for your state tax return is asking for the federal Submission ID, it will probably work. It's worth a try. If you filed your federal tax return with TurboTax you can call TurboTax support to get your Submission ID (SID). See the following link.
How do I contact TurboTax?
If they don't recognize the term Submission ID, tell them it's the "DCN / MeF Submission ID."