The onus is on the ower of the pet to keep that pet controlled (as required by law, usually at BOTH the city and county ordinance level) and OUT of the lanes of traffic (where cars belong, and dogs do not). Same thing often applies to children who run out into the street, or people who are jaywalking across streets instead of using the designated areas meant for pedestrians. In such cases it's very rare for even a ticket to be written to the driver, unless there was some eggregious circumstance such as DUI playing a factor or unless some substantial evidence of other wrongdoing on the part of the driver can be shown (ie unless you've got 40 yards of skidmarks to show that the vehicle was obviously traveling well above the posted limit).
As noted, if there was damage to the car, you could be liable for those damages, if your "property", in the form of the dog, was in the traffic lane where it shouldn't have been.

