Massachusetts officials yesterday alleged that E.F. Hutton & Co. misrepresented the value of a stock offering and said all the firm's offices in the state could be ordered closed unless restitution is made.

Secretary of State Michael J. Connolly issued an order notifying Hutton and 11 of its present and former agents that their registrations to do business in the state could be revoked unless the firm refunds investors' money in mining company stock and allows an independent audit of its books.

Connolly's office alleges that 84 Massachusetts residents invested more than $433,000 in Cadillac Explorations Ltd. of Calgary, Canada, from 1982 to 1984. The office said the company was declared bankrupt by the Supreme Court of British Columbia in September 1984.

Connolly's order alleges that Hutton failed to state when it solicited stock purchasers that Hutton's information on Cadillac Explorations and its recommendation to buy the stock were two years old.

It also said Hutton failed to verify whether projections in Hutton's information about the company had been realized.

In addition, it said Hutton misrepresented information investors relied upon by telling them that the Hunt brothers of Texas owned $50 million of Cadillac stock -- half the company -- and that the Hunt brothers' participation insured success.