SAN FRANCISCO—A federal appeals court has declined to decide whether telecommunications companies can be sued for helping government terrorism investigators eavesdrop on their customers without a warrant.

The U.S. 9th Circuit Court of Appeals sent a lawsuit against AT&T back to a trial judge to consider in light of a new law that shields telecommunications companies from such legal attacks.

Some 45 other lawsuits against other companies were awaiting the outcome of the AT&T case. Those legal challenges essentially ended in July when Congress overhauled bitterly disputed rules on secret government eavesdropping.