Why do you have two apartments? As others have said, you don't get to decide residency, for income tax purposes, based on the best tax rate. It depends on the details of your living and working situation including your intentions.
That said, Dublin has a 2% city income tax levied on earned income for those that either live or work in Dublin. If you are a Dublin resident, you are liable for the tax regardless of where the money was earned.
Even if you are not a resident of a state, you are liable for income tax on income earned in that state. So, a non resident return is usually required. The resident state will give you a credit, or partial credit, for tax paid to the other state
Ohio income tax rates:
http://www.tax.ohio.gov/ohio_individual/individual/annual_tax_rates.aspxCT rates:
https://www.tax-brackets.org/connecticuttaxtable
