No. PRS is not authorized to provide work permits.
A work permit applies to employees under 16 working during school hours. PRS cannot provide a work permit because it must be issued by the district superintendent or someone designated by the superintendent. Simply tell the employer that your child is homeschooled. PRS can provide a letter stating that your child is homeschooled through PRS if a potential employer requires verification.
For more details, see Colorado Department of Labor Youth Law