A member of the UN staff (not American) is found murdered in the New
York UN building.

Who would do the murder investigation and how would it proceed?

Also if someone where charged with the Murder, where and by whom would
he/she be tried?

Mongolia

Hey mongo...have you been hanging out with jeraboo by any chance?

And somebody is going to suggest we are the same people :-)

From the horses mouth.

An international territory
The site of UN Headquarters is owned by the United Nations. It is an
international territory. No federal, state or local officer or
official of the United States, whether administrative, judicial,
military or police may enter UN Headquarters except with the consent
of and under conditions agreed to by the Secretary-General of the
Organization.

However, the United Nations is bound by an agreement with its host
country to prevent its Headquarters from being used as a refuge for
persons who are avoiding arrest under the federal, state or local laws
of the United States or who are required by the Government of the
United States for extradition to another country or who are trying to
avoid the servicing of a legal process.


http://www.un.org/geninfo/faq/factsheets/FS23.HTM

The FBI (Federal Bureau of Investigation) would be invited by the
Secretary General to perfom the investigation. In the interest of
international diplomacy, police elements from the host nation of the
victim as well as Interpol would be involved as well.

The trial would be at a location suitable to the Secretary and the
victim's host nation. It might be in the US but some nations do not
allow the death penalty. If the US stated it would not remove the
death penalty from the trial options, the trial would likely be in The
Hague or Helsinki.

The extradition procedure would be interesting if the murderer is a US citizen.

Lets say the perpetrator is an American and he wipes out the entire
Iranian delegation. The US has no extradition treaty with Iran and
doesnt even have diplomatic relations. The crime is not commited in
the US or against a US citizen, so how does this individual get
charged and by whom?

I have not read it, but I wonder if this work of fiction might be helpful:

http://www.amazon.com/Murder-at-UN-novel-suspense/dp/0396073514

Jeraboo...my link still answers your question...

"the United Nations is bound by an agreement with its host
country to prevent its Headquarters from being used as a refuge for
persons who are avoiding arrest under the federal, state or local laws
of the United States"

But, I'm not suggesting he's using the UN as a refuge. I'm wondering
what authority/jurisdiction would arrest and charge him and with what
charge.

Some interesting though confusing comments about my question. The fact
that the UN can not be used as a refuge is not totally relevent to my
question. If someone were found murdered in the UN building there
would be presumably be a process which would kick into place in order
to identify the murderer.

the comment by MARKVMD sounds a reasonable one. However when I did the
little tour of the UN, the guide was at pains to stress that any
outside security agency only got invited in at the request of the UN.
This may mean one of two things -The UN in NY have their own internal
security who would do the initial investigation  - OR  as MARKMVD
points out the FBI would indeed be invited in
-it just maybe the UN authorithy does not wish to advertise this fact.

Jeraboo also brings up the very relevent issue of the victim's nationality.
(He takes the case of the victim/s been Iranian). Lets say the victim
was British - would Scotland Yard be involved? And lets say the
murderer was Laotian Would this person be extradited to England to
stand trial at the Old
Bailey

Or what if the victim were Cuban and the murderer was caught
red-handed in the UN building and it turned out the murderer was
British? what then would happen?

Canadianhelper When you say from the Horse's mouthare you saying you
work for the UN?

Regards

Mongolia