The post by brettd covers well the need for and funding concepts regarding forensic science in our criminal justice system. The question is moot since forensic science services are already paid for by tax payers. Police agencies have their own forensic science units, funded through city property taxes.
Medicolegal Death investigation is undertaken by medical examiner or coroner offices throughout the country. These are usually county facilities, whose budgets are paid for by county residential property taxes. The coroner does the autopsies and pays for the forensic testing of samples. Like cities, the county sheriff departments have CSI units as well.
Forensic science is very much a part of our criminarl justice system, and is already funded by the tax payer. There is concern that if private funding were used there could be an unfair application of resources, and therefore occurrence of injustices.
That being said, there is now a somewhat unfair situation in that only certain accused defendants or convicted criminals receive private funding for their defense to hire a so-called "dream team".