It depends on the state.
Many states acknowledge a federal extension while others have their own process.
To see how to file for an extension in your state, click the link below:
See this link to find your state.
https://www.irs.com/articles/state-tax-extension-information
https://turbotax.intuit.com/tax-tips/tax-extensions/how-to-file-for-an-extension-of-state-taxes/L6Fm...