Absolutely add it to your agenda for next general meeting. You need to meet this head on. Simply put, explain the situation to the membership, say under no circumstances will the board with threatened or bullied to remove a member and say that any/all future letters from this person will be turned over to the police.
Regarding removing a child from school... don't even touch that topic. Only address the PTO part of the letters.
This person sounds toxic... if you know who they are, confront them alone, express your feelings and tell them straight out to knock it off.

Remove a child from the school? That sounds like something the principal (or superintendent) should handle.

As to removal of an exec member, I'd suggest putting it on the exec board agenda and debating (a) whether to accept anonymous letters as a matter of policy, and if so (b) whether there is sufficient merit to the charge to warrant a vote. If it really overlaps with what was said at a previous meeting, you can just say that someone would need to motion to re-open the discussion.

The letters are going to other parents on the board. The letters are trying to remove an exec member and their child from the school, based on a phony reasignment. This is totaly false. The wording in letter sound very familiar to stuff said in a recent PTA meeting.

Who are the letters going to? Teachers? Principal? What is the nature of the content?
Is the content encouraging the readers to raise a stink to change a particular policy or is it just unproductive ranting? Is the topic matter even anything that the board has control over?

Depending on the nature of the letters, you may do well to ignore them and let the coward spout off without satisfaction of seeing the board get into a panic. If the letters have any merit, you could initiate a conversation at your next board meeting on the topic and see where everyone stands on it. During that conversation, you could also remind board members that failure to raise issues of this nature in the appropriate venue (a meeting versus nasty anonymous letters) is a violation of the board's ethical standards and that anyone caught violating the standard is subject to dismissal from their board position.

Problem: Someone is sending nasty anonymous letters around our school, attacking someone on the Exec Board. I think I know who it is, not a 100% sure though. It's someone close, that I know, maybe on board also!! What do I do ? Anyone here experienced this kind of stuff ? I appreciate any advice I can get..