Many states have their own state bureaus of investigation and their own investigators. Also, most states will have their own labs. Again, you'll find the same types of support opportunities here as at the federal level. You'll have to contact your own state agency or check if your state has it's own online bulletin board. The educational requirements will vary between high school diploma and college degree.
Big cities have their own police forces, their own investigators and detectives.
Of course, you'll have to rise up through the ranks from patrol. It is unlike the federal level in that respect. In the federal level, you'll start right out as investigator. But there is something to be said for learning the law enforcement process from the streets on up. Again, as with State and Federal agencies, you will find the same types of support positions.