The first case against General Motors Co. over its faulty ignition switches can proceed to trial after a federal judge rejected the auto maker’s bid to dismiss the allegations in the case outright.

U.S. District Judge Jesse Furman in Manhattan said Wednesday that GM’s arguments “fail as a matter of law.” GM argued that the plaintiff, Robert Scheuer, cannot prove that the ignition-switch defect or GM’s conduct caused his injury.

The allegations regarding the company’s conduct open GM to the possibility of punitive damages. A jury trial is to begin Jan. 11.

Mr. Scheuer’s case is the first of the so-called bellwether cases in the GM ignition-switch lawsuits, which are linked through a multidistrict litigation. A bellwether case is selected to test arguments and gauge possible recoveries for other similarly situated plaintiffs in an attempt to reach a large-scale resolution.

This is the first of six bellwether cases scheduled to move forward throughout 2016, with a trial for the last case to take place between Nov. 14 and Dec. 2.