New Yorkers would be allowed to ride the rails and city buses with their pets out in the open during emergency evacuations under a bill sent to Gov. Andrew Cuomo’s desk.

The measure allows residents to “board any commuter transportation” with their pets “in the event that a state of emergency has been declared and an evacuation of any region of the state is in progress.”

Under current MTA rules, pets have to be “enclosed in a container” on public transportation unless they’re service animals, a no-go for residents with large furry friends.

Cuomo has until Oct. 23 to sign the bill, which was sponsored by Assemblywoman Linda Rosenthal (D-Manhattan).

She introduced the measure after many pet-owning New Yorkers chose not to evacuate their homes in the midst of Hurricane Sandy.

“I observed that during a lot of natural disasters that people wouldn’t leave their homes unless they could take their animals with them,” Rosenthal told The Post.

“We saw that with Katrina. We saw it with Sandy,” she said.

In a memo accompanying the bill, she added that refusing to evacuate puts lives at risk.

“This situation to refuse evacuation not only jeopardized the lives of residents and defenseless pets, but also emergency personnel struggling to evacuate them,” said Rosenthal, who owns two cats.