The Intergalactic Police appeared in the episode “Pinewood Derby”.
In “Pinewood Derby”, a supposed intergalactic criminal named Baby Fark McGee-zax holds Earth hostage after discovering a "warp drive" made out of a superconducting magnet Randy Marsh stole from the Large Hadron Collider.
After hearing the Intergalactic Police approaching, he drags Stan Marsh out of sight and cloaks his ship. The Intergalactic Police question the town of South Park, asking if they have seen McGee-zax, as he stole a large sum of "space cash". Fearing for their lives, as well as Stan's life, they do not admit to seeing him.
Shortly afterwards, McGee-zax returns, and at Randy's urging, Stan reluctantly stabs him in the neck with a makeshift shank. Later, after Earth's world leaders decided to keep and distribute the "space cash", the Intergalactic Police return, revealing that McGee-zax was not a criminal but an "Ambassador of New Planet Testing", and that he faked his death.
The whole incident was a test to see if Earth was worthy of joining the intergalactic community. They mock the Earthling's stupidity and reveal that Earth failed the test. They then board their ship, lock Earth as well as the moon in a type of force field in order to prevent it from ever communicating with the intergalactic community, and leave.
The aliens have two faces on one head, four eyes, and two mouths with one of them having a mustache.