Not by e-filing. Tax regulations require that a state return cannot be filed unless a federal return is e-file the first or at the same time. This is a security precaution, because in the last few tax seasons, there was significant fraud claimed by people filing state returns without a matching federal return, because the states had weaker security procedures.
You could e-file your federal and state returns at the same time, and select “I will pay by mail“ for your federal return, so that you do not make a payment at the time of filing. Then, when you receive your state refund, you could make the federal payment. However, as noted by others, you will still need to pay your federal tax debt even if your state refund is delayed.
Also, you are asking the question in August 2023. Your tax payments were due April 17–even if you had an extension to file, you were still required to pay on time. The penalty for failing to pay your tax bill on time is about 1% per month. If you did not have an extension on the deadline to file, the penalty for late filing and late payment is 5% per month for the first five months and then 1% per month after that. If you file now but don’t pay your federal taxes due, you can expect the penalties and interest to continue to accrue until you eventually do pay it.
