Hair products that are regulated as cosmetics are allowed to declare ingredients on the outside box only (See Title 21Code of Federal Regulations (C.F.R.) Section 701.3(b)). Please note: If the hair product is regulated as a drug (e.g., a dandruff shampoo), different ingredient labeling rules will apply.

You mentioned a possible emergency if the product is accidentally ingested. If the product is potentially hazardous to health, a Warning Statement is required. 21 C.F.R. 740.1 establishes that a cosmetic's label must bear a warning statement "whenever necessary or appropriate to prevent a health hazard that may be associated with the product." The Warning Statement must appear on the label so as to be conspicuous "under customary conditions of purchase and use." (See 21 C.F.R. 740.2.) Therefore, the Warning Statement must appear on both the outer box and the jar. If a particular ingredient is the source of the health hazard, the identity of the ingredient arguably should be included in the Warning Statement to facilitate medical treatment. For example, "Caution: Contains (insert name of ingredient). Do not ingest. If ingested, seek medical attention immediately."

These rules apply to all cosmetics sold in interstate commerce in the U.S., whether produced domestically or imported.