I suspect they want to do something outrageous and be unique in family lore.
I knew a guy who swore he’d be buried dressed like he lived.
His wife and kids buried him in a crappy stained sweatshirt. I’m sure they’re still talking about how ol’ dad was laid out.
I’m aware of nothing under Ohio law that would prohibit you from providing in your will that you be tattooed postmortem, and a quick Google search reveals nothing against it, either. As a practical matter, I’d suggest you make your wishes very clear to your executor, next of kin, funeral director and tattoo artist ahead of time, so that everyone knows what’s up and is less likely to balk when the time comes.
Yes, surely it’s up to the next of kin and/or executor to actually have it done, should it be legal and practical.
This. Regardless of your wishes, odds are that they will not be carried out unless both the executor and the next of kin are onside when the time comes. So talk to your next of kin, and choose your executor carefully.
And they’re also not going to be carried out unless you have a tattoo artist willing to carry them out. So find one.
And, as others have pointed out, it may be impractical or illegal to transport your cadaver to the tattoo artist’s parlour for the work to be done, so the tattoo artist will need to come to wherever the cadaver is — mortuary, funeral parlour, whatever — and do the work there. So check that your chosen tattoo artist is willing and able to do this. Plus, of course, the agreement of the owner/operator of the place concerned will be needed, so get them onside too.
I think the health department might have thing or two to say about it.
There are laws that pertain to the funerary business. I suspect they are strict.