See quotations.
1857. Let such men but have a sure thing, or, as Californians say, the deadwood, and they will bet their last farthing.San Francisco Call, Jan. 7.
1858. I have the dead wood on him was used familiarly [in Kansas], meaning: I have him in my power.A. D. Richardson, Beyond the Mississippi, p. 134 (Hartford, 1867).
1872. He considered himself to possess the dead-wood.C. King, Mountains of Sierra Nevada, p. 211. (N.E.D.)