"Criminal Investigation Department" appears to be fine for the rest of the English speaking world outside the US. The FBI is definitely not the "Kripo". If one looks at the hits for:

http://www.google.com/search?num=100&hl=en&lr=lang_en&q= "cr...

http://www.google.com/search?num=100&hl=en&lr=lang_en&q= "cr...

http://www.google.com/search?num=100&hl=en&lr=lang_en&q= "cr...

http://www.google.com/search?num=100&hl=en&lr=lang_en&q= "cr...

nearly every country in the world turns up, however the use of "Criminal Investigation Department" in the US seems to often be restricted to the investigative arms of Federal agencies like the IRS or DEA.

For the normal "Kripo" usage as here in Germany, in writing for US consumption, the decision is not so easy, because every major city has its own terminology.

For Los Angeles, there are two organizational groups that seem to handle "Kripo"-style investigation: the "Detective Services Group" and the "Criminal Intelligence Group", as shown here:

http://www.lapdonline.org/

For Chicago, it looks like one group for "Kripo"-style investigation: the "Bureau of Investigative Services", as shown here:

http://www.ci.chi.il.us/CommunityPolicing/AboutCPD/Organizat...

For New York, there also appears to be one group for "Kripo"-style investigation: the "Detective Bureau", as shown here:

http://www.ci.nyc.ny.us/html/nypd/html/db/mission.html

If you checked other large US cities, you would probably get even more titles.

For worldwide use, terms like "department", "bureau", "group", or "force" might be too restrictive or local. Something explanatory like:

"police criminal investigation authorities"

or

"police criminal investigation organization"

might be good.

HTH

Dan