There's one problem with the title:
She wasn't. Her husband was on the run. She was trying to find him. Technically, Woman Running After Man On the Run, but that wouldn't fit on the marquee. The Woman is Ann Sheridan, whose hair was creased by a large artillery shell:
I'm usually fond of her work, but she's mopey and hard-edged and standoffish here - as the role requires, I suppose, but she's no fun.
Guest appearance by Adam Lambert:
The plot concerns a man who takes it on the lam after he witnesses a murder, and the Intrepid News Reporter who helps her find her husband. A bit of a grind at first, enlivened by a few characters and some hard dialogue, it begins to enter Tilty Noir World about half-way through:
Before you know it, there are venetian blinds, your guarantee of noir:
And then there's a twist, and a good one, too. It redeemed itself by the end, and repays the time spent. One more note: Ann attempts to evade the cops by giving her dog some inedible food, so she can take him to the vet. The cupboard is interesting: sixty years later, I have these exact two items in my shelf. They haven't changed a bit.