The Bureau of Justice Statistics puts out a report on Law Enforcement Management and Administrative Statistics that contains data on local and state law enforcement agencies with more than 100 officers. Unfortunately the most recent one is from 2000. You can find it here: http://www.ojp.usdoj.gov/bjs/abstract/lemas00.htm Check the personnel tables they have a listing for officers per capita. Again this is just for agencies with more than 100 officers, so it won't really help with the lowest number per capita, and it's five years out of date.

I did find a 2004 press release from the Bureau of Justice Statistics that states: "Vermont had the fewest state and local sworn police officers per capita (15 per 10,000) and New York had the most (39 per 10,000)." You can see the press release here: http://www.ojp.usdoj.gov/bjs/pub/press/jeeus01pr.htm