It is not necessary in this case. Both are valid; only one can be appropriate, as RegDwight said.
I can offer you my opinion regarding what kind of message each variant might send:
The Physical Therapists' Organization could cursorily suggest ownership or investment, i.e. that its members would be stakeholders in the organization, either through investment or accreditation. Accredited or subscribing physical therapists stand to benefit from the organization, are responsible for its administration, and have access to its perks.
The Physical Therapist Organization implies affiliation and provision; the organization was formed for all physical therapists, perhaps to provide an easy means of networking, comparing notes and finding support.
So, depending on the nature of the organization, i.e. whether it is a closed or an open group, you could pick which sounds best. Of course, this is very subjective.