I can provide a little context for the origin of anthropometric indicators, like fingerprints, in the forensic setting, but the legal precedent that established/validated fingerprint use is outside my area of expertise.

Despite the popular link between fingerprints and identification in modern forensic settings, fingerprints were not the first standardized attempt to identify criminals or exonerate those under suspicion of crimes. At first, attempts were made to identify criminals based on unique features. Files for the British Register of Distinctive Marks, for example, included information on the location and number of birthmarks, scars, and tattoos. To a certain extent, this inventory of distinctive marks continues in the modern setting, where prison officials photograph and catalog tattoos to aid identification of suspects. Another method of identification, developed by Bertillion, was based on ten anthropometric measurements, like check width and length of the right ear, that could be cataloged and used to identify repeat offenders.

The use of fingerprints in the forensic setting went through several starts and stops. Fingerprints were used for general identification during the 1860s in India, and in the 1880s in Japan Dr. Henry Faulds used fingerprint comparison to exonerate an aide of burglary. However, it wasn't until the publication of Francis Galton's Royal Institution papers, which developed a classification system for fingerprints and estimated the likelihood of any two people having the same fingerprints, that the field began to grow. Galton estimated the chance of two people with the same prints at 1 and 64 billion (giant PDF warning, but view Galton's paper Finger Prints here). In the early 1900s the New York City police department became the first in the United States to catalog fingerprints of criminals.

For more info check out Cole (2004) History of Fingerprint Pattern Recognition.