I'm only treasurer for a couple more weeks. To be precise, I won't even BE treasurer of this new PTO. We are switching from a PTA to a PTO. As part of the executive board, I have been left out of every decision and discussion concerning this transition, I do NOT have a good relationship with the presidents. Frankly, I don't want to be legally responsible for anything having to do with the new organization by having my name on the documents. But the presidents are insisting it's MY job to do all this work.
There really isn't any hard and fast rule regarding who is responsible for what that will apply to every Parent Group. In one group the treasurer might be responsible for all of this stuff, in another group it might all fall to the president, and in another it could be done by the board as a whole. Every group is different and and divides up officer duties differently.
In our group, the treasurer would most likely be in charge of all of those things officially, although unofficially we'd probably just sit down at a board meeting and start slogging through the paperwork until it was done without regard to job title.