A Crup is a wizard-bred creature that strongly resembles a Jack Russell Terrier, except that a Crup has a forked tail.
Crups are incredibly loyal to wizards and ferocious towards Muggles. They will eat almost anything. When a Crup is six to eight weeks old they are required by law to have their tail removed, using a painless Severing Charm, in case they are noticed by Muggles (FB).
A license from the Department for the Regulation and Control of Magical Creatures must be obtained to own a Crup. The owners must also pass a test to show that they are capable of controlling the creature in Muggle inhabited areas (FB, JKR-W1).
They came up quite often on Ordinary Wizarding Level examinations therefore they were part of the Ministry of Magic approved curriculum at that level (OP15). In 1996, Rubeus Hagrid‘s fifth year Care of Magical Creatures class studied this creature (OP25).
According to the W.O.M.B.A.T. it is possible for a Crup to interbreed with a dog (JKR-W1).
President Thornton Harkaway of MACUSA owned a pack of Crups, but he could not control them and they managed to wound several No-Majs in Williamsburg, Virginia, which was considered a breach of the International Statute of Secrecy. The bites of the Crups caused the victims to bark like dogs for forty-eight hours. Harkaway was forced to resign from office (MNA).
As an English word, "crup" is an alternative version of "croup," which denotes the rump of a horse (source: Wiktionary) or other animal (source: Wiktionary). A "crupper" is a piece of saddle equipment that goes around a horse's tail (source: Wikipedia).
From the Web
Pottermore: Magical Congress of the United States (MACUSA) by J.K. Rowling