Generally, a beneficiary does not owe income taxes on assets received from a decedent. There are some exceptions however. One called "income in respect of a decedent," relates to things like IRAs or US treasuries or US bonds. You do not seem to have any of these, but any interest earned on the bank account or CD earned after death would be taxable to you.
Hope this helps.
Mr. Fromm is licensed to practice law in PA. The response herein is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that if known could significantly change the reply unsuitable. Mr. Fromm strongly advises the questioner to confer with an attorney in their state in order to ensure proper advice is received.
The estate or the individual inheriting the money would pay income tax on the interest earned on the money in the bank account, provided it is not an IRA account. If it is an IRA they may owe income taxes on the entire sum.
There may be federal and Ohio estate taxes as well depending on the size of the estate.