Parent Organizations could easily find themselves navigating a mine field budgetarily and politically when it begins to give condolences in the form of gifts (fund donations or flowers). How will your organization draw the line to determine a policy on the type of loss that is considered "worthy" to note versus "not worthy" to note? Only children who lose a family member to violent crime, but not children who lose a family member to an illness? Only administration members whose elderly parent passes but not teachers whose elderly parent passes? What about the aids, cafeteria employees, and janitorial staff? They have families too and usually don't get the kind of attention the admin/teachers do in these matters.
What about school families going through dire financial straits due to medical bills or job loss -- will the parent organization do something for them (perhaps organize a benefit)?
Then, what about marking the happy occasions in life affecting the administration, faculty, and staff -- marriages, births, adoptions, promotions, achievement of higher degrees, and on and on...
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Because the parent organization's mission is typically related to improving education and because the organization could quickly find itself in a quagmire regarding condolence gifts, I recommend you steer clear of it altogether.
As an alternative, consider buying a box of all-occasion cards, and as circumstances dictate, have the board members sign and send the cards.
Our PTO has a "sunshine fund" in our annual budget, and we used some money from that fund for this purpose (two mothers of 3rd graders died of cancer last year).
What policies do you have in place to deal with life events for your students? We recently had a student whose mother died. He will not be returning to our school, but there is a debate about if we should donate money to a fund that was established for the student. In many cases the PTA doesn't learn of parental loss, but in this case a violent crime was involved, so it was also sad evening news.
Also, do you apply the same policies to those of school faculty and staff?