Her Word Against His

Laura's car is visibly damaged by hitting the deer. She either abandons the car or arranges to have it fixed, which any decent investigator would have discovered. The deer didn't get up and walk away, although they sometimes do, but she clearly did not drag it off the road of her own accord, so it would have been reported. The investigator, having found the first piece, would have looked for evidence of it near the country home and surely found the second piece that would have placed her vehicle on a road she claimed to have not been on or anywhere near.