No. In 1910.146(c)(1), The employer shall evaluate the workplace to determine if any spaces are permit-required confined spaces (PRCS). OSHA does not explicitly require that the evaluation be documented.
However, it is best practice. By documenting the PRCS evaluation process, it helps the employer share the hazards with contractors, saves time in determining hazards for reclassification for alternate entry, and is a good tool to share when training employees. It helps employees understand the specific hazards of the space they are entering and isn’t relying on an individual to share at the time of entry.