California:

https://nrm.dfg.ca.gov/FileHandler.a...27&inline=true page # 10 Updated 02/09/2013 JCO

§671. Importation, Transportation and Possession of
Live Restricted Animals.
(a) It shall be unlawful to import, transport, or possess
alive animals restricted in subsection (c) below except under
permit issued by the Department of Fish and Game. Permits
may be issued by the department as specified herein and for
purposes designated in Section 671.1 subject to the conditions
and restrictions designated by the department. Except
for mammals listed in Fish and Game Code Section 3950 or
live aquatic animals requiring a permit pursuant to Fish and
Game Code Section 2271, no permit is required by this section
for any animal being imported, transported, or possessed
pursuant to any other permit issued by the department. Cities
and counties may also possession or require a permit for these
and any other species not requiring a state permit.
(b) The commission has determined the below listed animals
are not normally domesticated in this state. Mammals
listed to prevent the depletion of wild populations and to provide
for animal welfare are termed “welfare animals”, and are
designated by the letter “W”. Those species listed because
they pose a threat to native wildlife, the agriculture interests of
the state or to public health or safety are termed “detrimental
animals” and are designated by the letter “D”. The department
shall include the list of welfare and detrimental wild animals
as part of DFG MANUAL NO. 671 IMPORTATION, TRANSPORTATION
AND POSSESSION OF RESTRICTED SPECIES,
to be made available to all permittees and other interested
individuals.
(O) Family Cichlidae-Cichlids
1. Tilapia sparrmani (Banded tilapia) (D).
2. Tilapia zilli (Redbelly tilapia) (D), except permits may
be issued to a person or agency for importation, transportation,
or possession in the counties of San
Bernardino, Los Angeles, Orange, Riverside, San
Diego, and Imperial.
3. Tilapia aurea (Blue tilapia) (D).
4. Tilapia nilotica (Nile tilapia) (D).

This section also goes into getting permits. O. mossambicus is not restricted.