I can point you to a source that states it is your responsibility to inform the IRS, assuming that whatever the state finds also increases your federal tax obligation.
When you sign (and this would include e-sign) your tax return, you sign a statement that says:
"Under penalties of perjury, I declare that I have examined this return and accompanying schedules and statements, and to the best of my knowledge and belief, they are true, correct, and complete. "
Look on Form 1040 where it says, "Sign here":
https://www.irs.gov/pub/irs-pdf/f1040.pdf
If it turns out that the State identified income that you did not report, it is likely it wasn't reported to the IRS either, so the statement signed that the return is 'true, correct and complete' is no longer accurate or truthful. Best to contact the IRS and says 'Oops, I need to correct my tax return." Better you tell the IRS before the IRS finds it themselves.
You have an obligation to correct your federal tax return if you later find something that would change what you fair tax obligation is, whether that is identified by a State audit or a mistake you caught yourself.
