The Centers for Disease Control and Prevention (CDC) has plainly said, "Do not operate gasoline-powered engines in confined spaces." Electric ice resurfacers have replaced gasoline-powered machines in some communities. Still, there's no substitute for working carbon monoxide detectors and proper ventilation. More data and recommendations in this excellent paper [Occup Environ Med 2002;59:224-233 doi:10.1136/oem.59.4.224] from 2002.
Only three states—Massachusetts, Minnesota, and Rhode Island—regulate air quality at indoor rinks.