No. You do not need to wait for your resident return to be accepted to work the non-resident state return. In fact it would have been better as @xmasbaby0 states to have completed the non-resident state return and then the resident state return and filed them all at the same time when complete. The reason is, typically you get a credit on your resident return for taxes paid to another state.
Your resident state taxes all income from all sources which includes income earned in a non-resident state. The non-resident state taxes income earned in it. Therefore you have been double taxed on some income.
To mitigate that double taxation you figure a credit on your resident return for the income tax on the double taxed income. You would work your non-resident return to find what income and income tax you paid and use those numbers to figure the credit for taxes paid to another state on your resident return.
Should your resident return be rejected for some reason you will be able to go back and figure the credit you missed. If it is accepted then you will need to work an amendment to get the credit. Again you'll need to work the non-resident return first to find the numbers to use on the resident return.
NOTE: There are some special circumstances where the non-resident state will give you a credit for taxes paid to another state and so you could use resident state numbers to figure the credit on your non-resident return. If you post what states are your resident and non-resident states someone will be able to let you know if you fall into one of the special categories.
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