I think if memory is correct, unless a priest is trained to be an exocist, he would not need permission.
For a prayer of deliverance (minor exorcism), he wouldn't; for a formal exorcism (major exorcism), he would (for more on that see
here and
here with reference to the applicable canon law). What he did in this case was kind of a half-baked, religion-neutral (no explicit mention of Christ), nonpartisan PC mix of a minor and major exorcism that was directed at cleansing the building.