You will need to check with your state to see if they accept state tax return filings with W-7s attached
State filing - You will want to file an
extension for your state until you receive your ITIN. This is because the
application for your ITIN is a federal filing. Most state will not process
your return without either a SSN or an ITIN. (However some states will
accept state filings with W-7 attachments. You will need to contact your
state's Department of Revenue and ask if your state will accept a state
tax return with a Form W-7 attached).
When
the IRS assigns you an ITIN, update your returns (both federal and state) in
TurboTax with this new information and then you should be able to e-file your
state return.
Because
many states give an automatic extension when you file the federal extension Form 4868, just file a
federal extension even if you don't think you will need it for your federal tax
return. But check with your state's Department of Revenue to make
sure that your state doesn't have a separate state extension filing. Here
is a link to all state's DoR: (to expand answer, select see entire answer)
https://ttlc.intuit.com/replies/3302452