The filing fee with a court is $175 and if you get the forms and file on your own that should be all you pay. But if you get an attorney to draft the forms it could cost anywhere between $500-1000.
3105.31 Causes for annulment.
A marriage may be annulled for any of the following causes existing at the time of the marriage:
(A) That the party in whose behalf it is sought to have the marriage annulled was under the age at which persons may be joined in marriage as established by section 3101.01 of the Revised Code, unless after attaining such age such party cohabited with the other as husband or wife;
(B) That the former husband or wife of either party was living and the marriage with such former husband or wife was then and still is in force;
(C) That either party has been adjudicated to be mentally incompetent, unless such party after being restored to competency cohabited with the other as husband or wife;
(D) That the consent of either party was obtained by fraud, unless such party afterwards, with full knowledge of the facts constituting the fraud, cohabited with the other as husband or wife;
(E) That the consent to the marriage of either party was obtained by force, unless such party afterwards cohabited with the other as husband or wife;
(F) That the marriage between the parties was never consummated although otherwise valid.