It might be cause for slander, but I don't see it as a civil rights violation.
I believe slander has to be with reckless disregard for the truth. If the storeowner has witnessed the person stealing, then it is not reckless disregard.
I in no way see this as violation of civil rights. What civil right is being violated? If the person's rep suffers, he has recourse to sue.
And why I had to endure 3 pages of narco-libertarian claptrap about rights is beyond me. We need better moderation.