It depends. Each state has its own filing requirement for nonresident taxpayers. Please view the filing requirements below.
Utah: Every nonresident with income from Utah sources who must file a federal return need to file.
https://incometax.utah.gov/instructions/who-must-file
New York: If your New York source income exceeds your New York standard deduction then you are required to file a nonresident state return.
https://www.tax.ny.gov/pit/file/nonresidents.htm
California: You must file a Califonia nonresident return if your income from all sources that is more than the amount defined in this chart.
https://www.ftb.ca.gov/individuals/FileRtn/index.shtml
Follow the directions in the TurboTax FAQ below if you need to file a nonresident state return. You must prepare your nonresident states before your resident state.
https://ttlc.intuit.com/replies/3302052