HELSINKI — Finland’s police are investigating whether a lawmaker had cheated Parliament out of over $14,000 in tax-free reimbursement after claiming allowances for a second home that turned out to be a Helsinki sauna.

The member of Parliament, Ville Vahamaki of the nationalist Finns Party, denied any wrongdoing in a statement.

The Finnish tabloid Iltalehti reported in July that he and another member of Parliament had been claiming elevated housing allowances for a sauna they had rented in the basement of an apartment building.

“In practice, I use it for laundry and so forth,” Mr. Vahamaki told the newspaper at the time.

Mr. Vahamaki is suspected of having defrauded Parliament of around 13,000 euros (about $14,800) in the form of unjustified allowances, the Finnish National Bureau of Investigation said in a statement, adding that he had paid the money back.