Mrs. O'Malley and Mr. Malone (1950).

Based on "Once upon a Train, or the Loco Motive" (1950) by Stuart Palmer and Craig Rice, the comic Mrs. O'Malley and Mr. Malone features Marjorie Main as a radio contest winner and James Whitmore as a lawyer who stumble over constant corpses on their train to New York. Note the sleuths are handcuffed together a la Robert Donat and Madeleine Carroll in The 39 Steps.