I think you will find that someone somewhere has a written policy. At a minimum, your actions will spark some interest and debate that should provide an appropriate foundation on which to build your policy. The best place to begin when writing an investment policy is the legal constraints that have been placed on you. From there you can decide whether you feel that further constraints are needed and whether the laws are strict enough. Consider the ramifications of losing principal due to inattention to basic research of statutory provisions or local ordinances, etc.
Informed decisions are the best decisions.
An investment policy, any policy, is the most important document you will produce as a governing body. It will put everyone on notice as to how funds are to be managed within the constraints set by you, the governing body. Not only is allocation a concern, but also diversification. The two topics cover the lion's share of investment decision-making. Allocation, in my view, refers to spreading risk across a specific time horizon - spread the time risk.