The State of Missouri does not require entry permits or any testing, they do however require a health permit within 30 days, and all goats must be free of any clinical signs of an infectious disease.

From the state website:

A. Goats must be free of clinical signs of an infectious or contagious disease. All goats, including wethers, must be accompanied by a Certificate of Veterinary Inspection showing official identification (eartag, electronicimplant, or registration tattoo) as defined in Title 9, Code of Federal Regulations, Part 79, January 1, 2008, herein incorporated by reference and made a part of this rule, as published by the United States Superintendent of Documents, 732 N Capital Street, NW, Washington, DC 20402-0001, phone: toll free (866) 512-1800, DC area (202) 512- 1800, website http://bookstore.gpo.gov. This rule does not incorporate any subsequent amendments or additions. If electronic implants are used for identification, owner/manager must provide electronic implant reader.
B. No tests or entry permits are required

MISSOURI STATE VETS OFFICE

Name: Dr. Taylor Woods
Title: State Veterinarian
Director of Animal Health Division
Agency: Animal Health Division
Department: Missouri Department of Agriculture
Mailing Address: P.O. Box 630
Jefferson City, MO 65102-0630
Office Address: 1616 Missouri Blvd.,
Jefferson City, MO 65109
Office Telephone No: (573) 751-3377
Fax No: (573) 751-6919
E-mail : taylor.woods@mda.mo.gov