No. Federal law specifically releases the leasing company from liability.
49 U.S. Code § 30106 Rented or leased motor vehicle safety and responsibility
(a) In General.—An owner of a motor vehicle that rents or leases the vehicle to a person (or an affiliate of the owner) shall not be liable under the law of any State or political subdivision thereof, by reason of being the owner of the vehicle (or an affiliate of the owner), for harm to persons or property that results or arises out of the use, operation, or possession of the vehicle during the period of the rental or lease, if—
(1) the owner (or an affiliate of the owner) is engaged in the trade or business of renting or leasing motor vehicles; and
(2) there is no negligence or criminal wrongdoing on the part of the owner (or an affiliate of the owner).
This is a result of the Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (Pub. L. 109–59), passed in 2005, due to cases where lessors were found liable.