Crows are covered under 2 portions of the regulations.
From 50 Code of Federal Regulations:
§ 20.133 Hunting regulations for crows.
(a) Crows may be taken, possessed, transported, exported, or imported, only in accordance with
such laws or regulations as may be prescribed by a State pursuant to this section.
(b) Except in the State of Hawaii, where no crows shall be taken, States may by statute or
regulation prescribe a hunting season for crows. Such State statutes or regulations may set forth
the method of taking, the bag and possession limits, the dates and duration of the hunting season,
and such other regulations as may be deemed appropriate, subject to the following limitations for
each State:
(1) Crows shall not be hunted from aircraft;
(2) The hunting season or seasons on crows shall not exceed a total of 124 days during a calendar
year;
(3) Hunting shall not be permitted during the peak crow nesting period within a State; and
(4) Crows may only be taken by firearms, bow and arrow, and falconry.
and
§ 21.43 Depredation order for blackbirds, cowbirds,
grackles, crows and magpies.
A Federal permit shall not be required to control
yellow-headed red-winged, rusty, and Brewer's
blackbirds, cowbirds, all grackles, crows, and magpies,
when found committing or about to commit depredations
upon ornamental or shade trees, agricultural crops,
livestock, or wildlife, or when concentrated in such
numbers and manner as to constitute a health hazard or
other nuisance: Provided:
(a) That none of the birds killed pursuant to this
section, nor their plumage, shall be sold or offered for
sale, but may be possessed, transported, and otherwise
disposed of or utilized.
(b) That any person exercising any of the
privileges granted by this section shall permit at all
reasonable times including during actual operations, any
Federal or State game or deputy game agent, warden,
protector, or other game law enforcement officer free and
unrestricted access over the premises on which such
operations have been or are being conducted; and shall
furnish promptly to such officer whatever information he
may require, concerning said ope rations.
(c) That nothing in this section shall be construed
to authorize the killing of such birds contrary to any State
laws or regulations; and that none of the privileges granted
under this section shall be exercised unless the person
possesses whatever permit as may be required for such
activities by the State concerned .
There is plenty of flexibility in the regs. But your best long-term solution is eliminating the food source and safe roosting area.