In Kentucky, the penalty for late filing of state income tax returns depends on the amount of tax owed and the length of the delay in filing. The late filing penalty is typically 5% of the tax due per month or part of a month that the return is late, with a maximum penalty of 25% of the tax due. Additionally, interest is charged on the unpaid tax at a rate of 2.67% per year. It's important to note that penalties and interest can vary depending on the specific circumstances, so it is recommended to consult the Kentucky Department of Revenue or a tax professional for accurate and up-to-date information regarding late filing penalties.