Please check with the Connecticut Department of Revenue to see if an online payment option is available. Please see this TurboTax FAQ, How do I contact my state Department of Revenue?https://ttlc.intuit.com/replies/3302452
Also, see this related TurboTax FAQ, What are my options for getting my state refund or for paying any state taxes I owe?https://ttlc.intuit.com/replies/3301663