Generally speaking an employer is free to not hire you for literally no reason at all, some prior wart on your employment history, something posted on facebook, or references which set off alarm bells or lack of prior references, or just some "sense" to move on. Unless its tied to a protected issue such as age, sex, race and perhaps some state specific taboos like height and weight --the employer can just move on, withdraw your offer, or fire you.
If somebody in your past is making false accusations of criminal conduct to others you may have a valid course of action against them for libel /slander