The Passenger by Lisa Lutz

She didn't do it, but when Tanya's husband ends up dead at the bottom of the stairs, she leaves. She dyes her hair, cashes in her credit card and takes a new identity as she flees town. This isn't the first time and it won't be the last. She's skipping from town to town, trying to escape from a past that she's not sure she can outrun in the end.