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The U.S. Equal Employment Opportunity Commission Compliance Manual advises that employers cannot enact a "blanket exclusion of persons convicted of any crime." Employers can reject an applicant with a criminal conviction if the employer can demonstrate that the reason was "job related."
EEOC Guidelines require employers to consider three factors: the nature and seriousness of the crime, how long it has been since the conviction and the type of job at stake. For example, a bank could legally reject an applicant with a robbery or forgery conviction, because these convictions are specifically tied to job requirements.
So the answer is yes, a felon can legally work at a school, but it would not mean that they would be offered a position. However, if the applicant was denied based solely on their criminal record, the applicant can file a discrimination claim with the EEOC to investigate to see if the grounds were justified or not. If they find the denial was not justified, then they can issue a "right to sue" letter that the applicant can use to file suit for discrimination.
I have researched this pretty extensively, and am unable to find anything under Arkansas law that would legally prohibit a felon from working on school property. So I would opine that unless some condition of the person's parole prohibited them from being on school property, then there is nothing that would legally prevent it.
Certain jobs that require a person to be licensed (nurses, law enforcement, etc.) can deny employment based on a felony conviction, but that is not the case here. Daycare employers can deny based on the "special position of trust" but once again, that is not the case here where the person would not be interacting with students.