Ted Hughes said there was little reason to follow through with the investigation following the former Justice Minister's resignation from the Legislative Assembly last month.
The Board of Management, a government body responsible for MLA expense accounts, filed an official complaint with Hughes in August after it was revealed Allen claimed to live in a shack outside of Inuvik without electricity or road access in order to qualify for a lucrative housing allowance.
Allen was ordered repay nearly $10,000 in public funds. Hughes was asked to examine whether his Inuvik housing claim amounted to a fraud against the government.
Allen was later found to be living full-time in Grimshaw, Alta., where his wife owns a house.
A byelection for Allen's seat is to be held this month.