That's pretty much it, in a nutshell: for all 50 states taken
combined, how many state police officers are there?  Exact number not
required --- a well-justified number within a margin of error of 5% is
fine.

Iswhatitis --

The Bureau of Justice Statistics does period surveys of state & local
law enforcement and the most-recent study gathered data from 2000. 
The study, called LEMAS for Law Enforcement Management and
Administrative Statistics, 2000 was published in 2004.  It is linked
here and the section "Personnel" has full-time employees by state on
p. 241:

Bureau of Justice Statistics
"LEMAS, 2000"
http://www.ojp.usdoj.gov/bjs/abstract/lemas00.htm

This will get you right to the section:
LEMAS Personnel, 2000
http://www.ojp.usdoj.gov/bjs/pub/pdf/lema001b.pdf

The total is 87,028.  Not surprisingly, California has the most with
9,706.  North Dakota has the smallest number, with 193.

Google search strategy:
"Bureau of Justice Statistics" state police

Best regards,

Omnivorous-GA

Excellent.  Good find!

This may help:
"Police and detectives held about 840,000 jobs in 2002. About 81
percent were employed by local governments. State police agencies
employed about 11 percent and various Federal agencies employed about
6 percent. A small proportion worked for educational services, rail
transportation, and contract investigation and security services."

Also see:
http://faculty.ncwc.edu/toconnor/polstruct.htm#STATE

I hope that helps.

Best regards,
Rainbow