Here in Connecticut, it would depend on the source of that $60k. If it were all social security, you wouldn't pay any income tax. If it were military retirement pay, you wouldn't pay any income tax. If it were from pensions, you wouldn't pay any income tax. And assuming you paid more than $300 in personal property tax, if it were all withdrawals from tIRAs, you would pay no state income tax. If it were wage income (and again assuming you paid more than $300 in property tax), your CT state income tax would be $1500. That's for 2023. In 2024, it would be about $1194.
All my numbers come from actually calculating the taxes using the relevant CT Department of Revenue Services tax forms for this year, with knowledge of how the law changes things for next year.
So, I would say your source is incorrect. I don't really blame them, because Connecticut taxes are complicated, due to a variety of credits, exemptions and thresholds, but they are still wrong