OLYMPIA — The state Legislature gave its final approval Tuesday to a bill aimed at allowing school nurses to administer a potentially lifesaving allergy medication in an emergency.

Senate Bill 5104 would allow public schools to stockpile epinephrine, a hormone known better by the brand name EpiPen that is injected to prevent or stop severe allergic reactions that can kill within minutes.

Under the bill, school nurses could use the epinephrine on any student, regardless of whether the student has been diagnosed with an allergy — a change from current law that only allows it to be used on diagnosed students.

The bill didn’t receive a single “no” vote in the state House or state Senate. Gov. Jay Inslee plans to sign it, according to spokeswoman Jaime Smith.

But in the run-up to the House vote, some lawmakers said the bill would have been better if it had allowed all school employees — not just nurses — to inject all students with epinephrine, as an original version would have.

State Rep. Chad Magendanz noted that school nurses often are assigned to cover three or five schools.

“This bill will save lives. My frustration with it is that it could save a lot more lives,” said Magendanz, R-Issaquah. “The fact that we will be able to save (only) one out of five lives, or one out of three lives, is almost criminal.”

Vancouver Democrat Monica Stonier said it’s important that those administering the hormone to undiagnosed students are trained.

The bill’s prime sponsor, state Sen. Mark Mullet, said he’s happy with the compromise he worked out with a school nurses professional organization. But the Issaquah Democrat said he may seek to expand the bill in the future.