It doesn't look like any of the petrified wood I have seen in this area. I was leaning towards some sort of sea weed or kelp like plant. A preserved mud flow definitely sounds logical looking at one of the sides. I just don't know enough to call either way. I wiped it down a little more, and here's one of the impressions I thought looked almost leaf-like
Leaves would present stems and veins, no? If this is plant matter, perhaps it is a thallus.
Take the object to the closest museum or university, and let us know what you find out.