Sonia (21), who returned from her in-laws' place soon after her marriage seven years back, left with Rina (20), who was a student at the former's tailoring school in Anauda village.
They left their homes on Saturday after they failed to convince their parents on their decision to get "married".
"Finding it difficult to persuade the parents, we called police for help," Sonia said.
"First, we tried to persuade them to change their decision. However, finding them firm, their parents were called at the police station," SHO Anil Kumar said.
"The family members of both the women have snapped the ties with them. The women have left for unknown place to stay in a live-in relationship," Deputy SP Sanjai Kumar said on Sunday.
He said legally they can be in a 'live-in relationship, as per a judgment of the Supreme Court.
Before leaving the police station, Sonia said they now would stay at an unknown place as they "fear danger to their lives from their relatives".