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Considering that you will filed married and claim 4 allowances -
Your net paycheck will be for $1,644.33 (this is after considering $131.64 for federal withholding, $119.23 for Social security taxes and $27.88 for medicare). No taxed for TN will be deducted.
If your employer withholds taxes for Ohio State than your net paycheck will be $1,579.73 (after OH tax withholding of $64.60)
If your employer does not withhold Ohio State tax, than you would normally pay quarterly installments to the OH State for the State taxes that you would owe
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.