can I sue for legal fees?

What is the name of your state (only U.S. law)? FL

The investigator told the states attorney that my case could not go criminal because there was no evidence to support the charges. The states attorney disregarded the advice of the investigator and pressed charges anyway. After I got out of jail some weeks later, I was able to produce enough evidence and testimony to have the charges dropped. Much of this evidence was already told to both the States attorney and the investigator. Is there a way to get any of my legal fees reimbursed or to get any compensation for 3 weeks in jail?

If the charging decision was made and the states attorney didn't have probable cause it would be malicious prosecution and you would be able to sue for your damages. What the investigator said is only one piece of evidence and you shouldn't rely on that alone.