I've never observed that there are more police because they don't have a military. It isn't a 'police state' by any stretch of the imagination. The one encounter I had with them was while wandering around the Casco Viejo, they were cruising around on bicycles and asked me if I needed directions; apparently a lot of them are on the tourist beat, just making sure that the areas are safe for ppl to be walking around gawking at architecture.
In terms of why they don't really need a standing military, you might just look at Panama's geographic circumstances; the southeastern border with Colombia is the Darien, a few hundred km of virtually impenetrable rainforest--not exactly the best way to conduct an invasion. And the western border is with Costa Rica, another country with no standing military; the border is also rather hilly and would be difficult going in force. Both coasts are rather heavily trafficked with fishing and pleasure boats, with noticable maritime police--the Coast Guard.
Military of Panama - Wikipedia, the free encyclopedia
Cheers.