Romance On The Run might rate better had it been done with some better production values. As it is Universal Pictures was doing a lot of cost cutting because the Laemmle regime had nearly bankrupted the place at this time.
When some jewels are stolen that are insured by Granville Bates's company, he always calls Donald Woods who recovers them for a fee and no questions asked. Woods is a guy who skips nicely over the dividing line of crook and detective, kind of like the Saint, but no one can prove a thing. Especially not William Demarest who isn't much smarter than Tom Kennedy in the Torchy Blane series. But he doesn't give up for lack of trying.
Through a bad combination of circumstances, Woods and man Friday Edward Brophy are chasing crooks Craig Reynolds and Grace Bradley through the USA south. Woods also has Patricia Ellis from Bates's office along for the ride and that's what the Romance On The Run is all about. Demarest is chasing all of them.
If this had been done at MGM with William Powell and Myrna Loy, Romance On The Run might well have been a classic. As it is it's an OK programmer, but nothing special.