Well, EPA is really more "systemic" risk of chemicals, I think. It regulates chemicals at point of production and use mainly to prevent systemic environmental issues later on.
I was mostly wondering who regulates this stuff for point of consumption by consumers -- OSHA is pretty clearly focused on production or use in business, not in the home, and CPSC isn't really so "sciencey" as OSHA or EPA -- it's more concerned with grossly apparent problems with products like swallowing magnets and decapitation in cribs.
I don't know who proactively looks for risks of products in long-term exposure/normal use on a long basis. Arguably the non-consumers with the most to care about that would be health insurers, so either an industry association of those or a regulator or a government insurer (medicare/medicaid) would have an interest in doing something like Underwriters Laboratories.
Not that health insurers do such a good job at anything that we really want them to expand to looking at home furnishings and such.
More info here. TL;DR: Gov't still trying to figure it out.
GAO was asked to review the approaches used under TSCA and REACH for (1) requiring chemical companies to develop information on chemicals’ effects, (2) controlling risks from chemicals, and (3) making information on chemicals available to the public. To review these issues, GAO analyzed applicable U.S. and EU laws and regulations and interviewed U.S. and EU officials, industry representatives, and environmental advocacy organizations.
GAO is making no recommendations.