You will need to contact your state directly to find out which installment plans they offer. Please see the below for a list of state department of revenues: https://ttlc.intuit.com/replies/3302452
How to File an Extension for State Taxes: https://turbotax.intuit.com/tax-tips/tax-extensions/how-to-file-for-an-extension-of-state-taxes/L6Fm...
