The fact that the charges were dismissed does not necesarily mean you can prevail in a civil lawsuit. I assume you would wish to sue for defamation claiming that a false statement was made and, as a result, you were damaged. The difficulties with such a suit are many:
(1) First, if you do sue, you can be deposed or may have to testify. If the allegations relate to a potential criminal event, you could be risking incriminating yourself where new charges would be filed;
(2) Second, if you siue, proving that a statement made was intentionally false and not simply wrong, is not easy. Moreover, charges may be dimissed for any number fo reasons;
(3) Finally, it would likely cost more to sue it out then the amount you are likely to recover.
I notice that you mentioned "the crown has with drawn all the charges", are you from Canada? Did this matter occur in Canada? If so it would be difficult for a Michigan attorney to advise you regarding your rights and remedies in Canada. This is a matter that you should discuss with a Canadian lawyer.