Voters on Tuesday said they don’t want Central Maine Power building a power transmission line through western Maine, and they said it resoundingly.

It’s not the final word in the Northeast Clean Energy Connect project, but the message could not be more clear.

Until regulators and the courts have time to resolve the outstanding questions over the project, CMP and their parent company, Avangrid, should respect that message.

They should immediately stop construction on the powerline corridor.

Instead, NECEC Transmission LLC, the company formed to shepherd the project, says construction will continue unabated.

The referendum passed Tuesday is “unconstitutional and violates both state and federal law,” a NECEC official said after the vote. The official also pointed out that the project has received every permit it needs after three years of review.

Court decisions will determine whether any of those statements hold true. Following Tuesday’s vote, NECEC filed a lawsuit in Maine Superior Court challenging the constitutionality of the referendum.

Meanwhile, the matter of the permits has been in court for some time, with a judge ruling that a state lease concerning a small tract of land being used for the corridor was awarded improperly.

The companies behind the project are appealing the decision, while the Department of Environmental Protection is considering whether to revoke the permit over the improper procedure.

The decision over the permit, delivered back in August by Superior Court Justice Michaela Murphy, put the future of the project in question even before Tuesday’s landslide vote against it.

Now it has an additional hurdle or two in front of it: a new state law that bans high-impact transmission lines in the Upper Kennebec Region, where NECEC is now being built, and requires legislative approval for any such project, retroactive to before the NECEC was proposed.

The soon-to-be state law is popular. Nearly 60% of voters cast a ballot in favor of Question 1, about 240,000 Mainers. And it is popular nearly everywhere: The referendum won in most municipalities across nearly all regions of the state.

Question 1 was successful largely because Maine voters don’t trust CMP following a series of customer service and public relations debacles.

But the landslide vote also came out of a desire to protect the forests of western Maine. Many people don’t want to see the corridor cut through the woods.

The courts may ultimately rule that the project must be allowed to move forward — that is, they might say that voters don’t have the ability to stop this particular project.

But after Tuesday’s vote, there’s no denying where the people of Maine stand. Even with the project’s fate still to be determined, that should matter.

There is no doubt about it: On Tuesday, Maine voted to stop the NECEC project.

While everything else is figured out, that should be honored.