No, liability coverages do not pay for the towing and storage costs for your vehicle.
Liability coverages of bodily injury and property damage pay for injuries or damages to other people that your vehicle caused. Liability does not cover damages, towing or storage fees for your vehicle if it has been in an accident.
Physical damage coverages of collision and comprehensive may offer these coverages, depending upon the terms of your policy. Or you may have had to add on a towing package for fees such as these to be covered by your auto insurer.
If you have questions regarding the type of coverage you have on your vehicle then read over the terms of the policy and discuss any questions or issues you have with your insurance agent who should be able to speak with you in detail about your policy.