With recent changes in the law it sounds like most exotic species are now protected and no longer fair game in Indiana. Guess you could only shoot the cougar in self defense.
312 IAC 9-3-18.5
Adds a new administrative rule that prohibits the taking of exotic mammals and intentionally releasing them
into the wild in Indiana. This new rule prohibits the hunting of exotic mammals such as fallow deer, elk,
antelope, and zebra in Indiana. Exotic mammals that are lawfully possessed would not be able to be
intentionally released into the wild in Indiana; if one escapes, a conservation officer would have to be
notified within 24 hours. Wild boar would be allowed to be taken at any time due to disease concerns and
the potential for damage to property. Other species of exotic mammals would be able to be taken by a landowner or tenant when causing damage to property. This new rule also authorizes the possession of exotic mammals from a family listed in this rule only as allowed by statute or administrative rule. This list of families of exotic mammals is designed to include all species of mammals found throughout the world that could potentially be possessed in captivity and hunted.
312 IAC 9-3-18.5 Exotic mammals
Authority: IC 14-22-2-6, IC 14-22-32-6
Affected: IC 14-22
Sec. 18.5. (a) A person must not take, as defined by IC 14-8-2-278, an exotic mammal that is a species
from any of the following families of mammals:
(1) Bradypodidae (tree sloth).
(2) Bovidae (gazelle, big-horn sheep, antelope, and wildebeest), except for domestic cattle (genus
Bos, including all dairy and beef animals) and buffalo (Bison bison).
(3) Camelidae (camel and llama).
(4) Canidae (jackal, wild dog, and other exotic foxes).
(5) Cebidae (marmoset).
(6) Cercopithecidae (baboon and monkey).
(7) Cervidae (elk, moose, caribou and other exotic deer).
(8) Dasypodidae (armadillo)
(9) Elephantidae (elephant).
(10) Equidae (wild horse and zebra), except for domestic horses.
(11) Felidae (mountain lion, lynx, tiger, and other exotic cats).
(12) Giraffidae (giraffe and okapi).
(13) Hippopotamidae (hippopotamus).
(14) Hyaenidae (hyaena).
(15) Lorisidae (potto and bushbaby).
(16) Macropodidae (kangaroo and wallaby).
(17) Manidae (pangolin).
(18) Mustelidae (otter, weasel, polecat and badger).
(19) Myrmecophagidae (anteater).
(20) Orycteropodidae (aardvark).
(21) Pongidae (chimpanzee, bonobo and gorilla).
(22) Procaviidae (hyrax).
(23) Procyonidae (ring-tail cat and coatimundi).
(24) Protelidae (aardwolf).
(25) Rhinocerotidae (rhinocerus).
(26) Suidae (wild boar and other exotic swine), except for domestic swine.
(27) Tapiridae (tapir).
(28) Tayassuidae (javelina and peccary).
(29) Tragulidae (chevrotain).
(30) Ursidae (bear).
(31) Viverridae (civet, genet and mongoose).
(32) A hybrid or genetically altered mammal of any of these families.
(b) Notwithstanding subsection (a), a person may take an exotic mammal only under one of the
following:
(1) the exotic mammal is taken by a resident landowner or tenant while causing damage to
property that is owned or leased by the landowner or tenant;
(2) the exotic mammal is a species from the family Suidae and has been released or escaped
from captivity or is a member of a breeding population in the wild; or
(3) the exotic mammal is a species from the family bovidae, camelidae or cervidae and
slaughtered in accordance with IC 15-2.1-24.
(c) A person may not possess an exotic mammal that is a species from a family listed in subsection (a)
except as otherwise provided by statute or by this article.
(d) A person may not release an exotic mammal that is a species from a family listed in subsection (a)
into the wild in Indiana except as otherwise provided by statute or by this article. A person must
report the escape of any exotic mammal listed in subsection (a) to a conservation officer within twentyfour
(24) hours.
(e) As used in this rule, "exotic mammal" means a species that is:
(1) not native to Indiana; or
(2) extirpated from Indiana and either:
(A) a wild animal; or
(B) a feral animal other than a dog or cat.
Just another night at work for me and Monty will be back here again bright and early. 
