That’s not a state law. Whether a primary is open or closed is at the discretion of the Party. However, the state law does prohibit voting in multiple primaries.
2013 Mississippi Code
Title 23 - ELECTIONS
Chapter 15 - MISSISSIPPI ELECTION CODE
Article 17 - CONDUCT OF ELECTIONS
B AFFIDAVIT BALLOTS AND CHALLENGED BALLOTS
§ 23-15-575 - Participation in primary election
Universal Citation: MS Code § 23-15-575 (2013)
No person shall be eligible to participate in any primary election unless he intends
to support the nominations made in the primary in which he participates.
http://law.justia.com/codes/mississippi/2013/title-23/chapter-15/article-17/b/section-23-15-575/