Question from one of my players.

Could you get a magical tattoo if you have a prosthetic arm?

I cant find any rules against it but at the same time you can remove a prosthetic arm, if that arm holds a magic tattoo - what happens to the magic then?

Under a strict application of the rules, magic tattoos can effect creatures like Autognomes and Warforged and thus there is no rules impediment to having them work on a prosthetic. 

The other question you have about the limb being removable is not answered under the rules, so it is up to you as the DM to work with your older to figure out how to answer the question.  You can go either way—you could say the magic is the important part, and the actual tattoo is just a marking, so the magic remains even if the prosthetic is missing, or you can decide the tattoo is what contains the magic and therefore the magic does not work if the limb containing the tattoo is not on the body. Entirely up to you and your player.

I'd say it doesn't work because Magic tattoos are inscribed on a creature’s body while a Prosthetic Limb is an item that replaces lost body part. One reason i would also rule against it is due to the fact that you can detach or reattach it, which would circumvent attunement.

Quote from Lagerquist >>

Question from one of my players.

Could you get a magical tattoo if you have a prosthetic arm?

I cant find any rules against it but at the same time you can remove a prosthetic arm, if that arm holds a magic tattoo - what happens to the magic then?

 I would keep it as simple as possible since the rules do not address this directly.

• You can tattoo the prosthetic because the prosthetic is magical and effectively becomes 'your' limb.
• For the sake of simplicity, I would rule that the magic remains in effect and you remain attuned when removing the arm, but after the period of a short rest the attunement breaks unless the limb is reattached, before the completion of that rest period.
• The tattoo becomes inert or, as at least one tattoo states, the tattoo is removed and becomes a magical needle again.
• Cursed tattoos would prevent the removal of the prosthetic.

Fairly simple answer. Can you tattoo a prosthetic arm irl? Didn’t think so. So unless it’s like a flesh arm sown onto the stump -wait that’s actually a kinda cool idea - it won’t work. You could paint it though. It just wouldn’t be a tattoo.

Quote from Jackthebackstabber >>

Fairly simple answer. Can you tattoo a prosthetic arm irl? Didn’t think so. So unless it’s like a flesh arm sown onto the stump -wait that’s actually a kinda cool idea - it won’t work. You could paint it though. It just wouldn’t be a tattoo.

 
I do want to reiterate to OP that the rules absolutely allow players to tattoo things you could not tattoo in the real world—as I mentioned in my first post, there are playable species made of metal that you can place magical tattoos on.  Accordingly, the “you cannot do it in real life, therefore you cannot do it in D&D” argument falls a bit flat in light of their existing usage under the rules. 

That is not to say the above reasoning couldn’t work for someone’s particular group—but if OP is going to say “no, you can’t tattoo your prosthetic,” they probably should come up with something better than “tattoos only work on flesh in the real world.”

Quote from Plaguescarred >>

I'd say it doesn't work because Magic tattoos are inscribed on a creature’s body while a Prosthetic Limb is an item that replaces lost body part. One reason i would also rule against it is due to the fact that you can detach or reattach it, which would circumvent attunement.

 I agree with Plaguescarred. Using the Tattoo on an item (Prosthetic Limb) wouldn’t work. And it avoids the OP’s issue of what to do if unattached. 

Important detail from the prosthetic limb

While the prosthetic is attached, it functions identically to the part it replaces. 

This would mean if you could apply a tattoo to the original limb, you could do so to the prosthetic replacement due to that identical functionality. We don't need a disability tax on magic items (which is the exact reason they removed attunement from the prosthetic limb in the first place)

Quote from Davyd >>

Important detail from the prosthetic limb

While the prosthetic is attached, it functions identically to the part it replaces. 

This would mean if you could apply a tattoo to the original limb, you could do so to the prosthetic replacement due to that identical functionality. We don't need a disability tax on magic items (which is the exact reason they removed attunement from the prosthetic limb in the first place)

 In that case then it would be up to the DM to decide if the effects of a tattoo on the Prosthetic limb would remain in effect, or not, if it were removed. 

Quote from Jackthebackstabber >>

Fairly simple answer. Can you tattoo a prosthetic arm irl? Didn’t think so. So unless it’s like a flesh arm sown onto the stump -wait that’s actually a kinda cool idea - it won’t work. You could paint it though. It just wouldn’t be a tattoo.

 Magical prosthetics and magical tattoos do not exist in real life. They do in this game.

Quote from Davyd >>

Important detail from the prosthetic limb

While the prosthetic is attached, it functions identically to the part it replaces. 

This would mean if you could apply a tattoo to the original limb, you could do so to the prosthetic replacement due to that identical functionality. We don't need a disability tax on magic items (which is the exact reason they removed attunement from the prosthetic limb in the first place)

 I read that to mean it can functionally do anything the replaced limb did, but it remains an item nonetheless, and a tatttoo is made on creature instead. 

In my campaign its how i'd rule it but other DM are free to allow it.