I could not find any definitive answers, but the following articles offer some context on how the term might have started.

An essay called "The Endless Dream Game of Death", by Luis Rodriguez states that the LAPD began using the term during the 1980's, to dismiss victims of gang violence.

In "NHI-No Humans Involved," UCSD faculty member Elizabeth Sisco, traces the use of the term to the San Diego area during the 1980's and 1990's, by San Diego police, to address a series of murders and sexual assaults against women. Sisco wrote that the head of the task force assigned to investigate the murders claimed that the use of "NHI" is fictionalized by old detective novels, but another San Diego officer confirmed the use of the "NHI" term in a Sacramento Bee article to describe these murders.

Rodriguez, Luis J. and D. Cesare (1995). Endless Dream Game of Death. Grand Street, No. 52, Games. pp. 61-77. http://www.jstor.org/stable/25007852. Access December 6, 2009 from Jstor database through San Jose State University.

Sisco, Elizabeth. (1993) NHI-No Humans Involved. NHI-No Humans Involved. Accessed December 6, 2009.