Teethers and teething toys intended to soothe a child (but not to ease teething pain) fall under CPSC’s jurisdiction and must comply with Section 4.22 of the U.S. Toy Standard, ASTM F963-17.
However, if your teether is primarily intended to soothe a child’s teething pain, your product falls outside the jurisdiction of the CPSC; instead falling under the jurisdiction of the US Food and Drug Administration (FDA). Please contact the FDA's Center for Devices and Radiological Health for more information on whether your teething product would be considered a medical device under their jurisdiction.
For more information on the requirements in place for your consumer product, please visit CPSC’s Regulatory Robot tool: https://business.cpsc.gov/robot.