A person that possesses any of the following animals shall register the animal in the same manner as provided in section 935.04 of the Revised Code:

1. (A) Pygmy, white-tufted-ear, silvery, and black-pencilled marmosets;
2. (B) Squirrel monkeys;
3. (C) Brown, white-faced, weeping, and white-fronted capuchins;
4. (D) Lemurs.