Hi John
Specific qualifications would probably differ according to which country you are based. I expect you would be required to take certification courses that cover, among other things, hazardous materials eg Pathogens, protection against them and the regulations of the Occupational Safety and Health Administration that govern crime-scene clean-ups.
There is a website you may find useful which lists three human qualities any crime scene cleaner requires: a strong stomach, the ability to emotionally detach from his work and a sympathetic nature.
Howstuffworks "How Crime-scene Clean-up Works"
You could contact some clean-up firms in your area to ask what they require.
I found it harrowing to know that about 20 to 30 families a year in the UK are currently left to pay for cleaning up their home after a murder.