Where is it required to obtain a permit or authorization to handle monarchs?

California and Washington both require a scientific collection permit for invertebrates. This includes any type of collection such as using them for scientific research or teaching, or collecting them to rear and release. 

California: https://wildlife.ca.gov/Licens...

Washington: https://wdfw.wa.gov/licenses/e...

In Mexico, it is illegal to touch monarchs, and in Ontario, Canada a permit is required to rear and handle invertebrates (including monarchs). In Nova Scotia, Canada, Monarchs have been listed as endangered, so they and their habitat cannot be touched without a permit.

There may be rules and regulations that we are not aware of that apply in additional states and provinces.