Using TurboTax you would have to print and mail the state estimated tax form and your check for payment.
TurboTax cannot be used to pay estimated taxes, federal or state.
Unless you are in New York state then you have some other options. See this TurboTax support FAQ for New York state estimated tax payments - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-payments/view-change-new-york-estima...
