If you are in, or sell to any other countries, then you do need to follow their regulations as well. Here are some resources that can help your research.
European Resources
www.childsafetyeurope.org/publications/info/child-safety-regulations-standards.pdf
Australia
www.productsafety.gov.au/product-safety-laws/safety-standards-bans/mandatory-standards
www.productsafety.gov.au/content/index.phtml/itemId/973519
Canada
www.hc-sc.gc.ca/cps-spc/legislation/acts-lois/ccpsa-lcspc/index-eng.php
www.hc-sc.gc.ca/cps-spc/pubs/indust/sleepwear-vetements_nuit/index-eng.php
MEXICO
https://www.profeco.gob.mx/english.htm