My tire on my suv was ruined when I ran over a road sign that was lying flat in the middle of the road. Is the state liable to reimburse me for the damaged tire since my auto insurance deductible will not be met?
You're out of luck; you'll will have to shoulder this one on your own.
States, Counties, Towns, and all other governmental entities have "immunity" against such occurrances and the liabilities flowing therefrom. In the absence of provable notice to the contrary, such entities are not liable or responsible for debris being in the roadways; e.g., signs, rocks, or anything else.