Does the person opening the Estate have to be living in Ohio?
Personal Injury Lawyer
The person would open it in the county where your father died.
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Car / Auto Accident Lawyer
This question is somewhat dependent on the laws in the State that you reside. Generally, yes, and Estate must be opened to pursue a malpractice/wrongful death lawsuit, and generally, the "personal representative," must reside in the State in which the Estate is opened, which again is generally where the decedent resided. There are some exceptions. You should consult with an estate lawyer on these issues.
I'm gathering from your question and your follow-up to the responses so far that your father was living in Ohio, but received negligent treatment in PA. This raises some fairly complex questions that are best answered by an attorney with experience with Pennsylvania and Ohio law. Depending on your circumstances, you may have as little as one year from the date of treatment to seek a recovery, at least with certain aspects of your potential claim. If you think there is a case, you should contact an Ohio or Pennsylvania personal injury attorney as soon as possible.