The US Department of Agriculture classifies Frogbit as an invasive plant. I've no idea if this carries any prohibition/penalty.
How I know this is a story. Some years back I wrote a series of aquarium plant profiles for another forum, and in the profile of Amazon Frogbit (
Limnobium laevigatum) included photos of the blossoms on my own floating plant which had been sold to me as the tropical Frogbit. The owner of the forum received an email from an official of the US Agriculture Department who had come across the profile/photo, informing him that this was an invasive plant, illegal in some states, and aquarists should not be propagating it. I looked into the matter, and discovered there are three near-identical (in leaf form) species that can only be told apart by their flowers, and obviously my plants were one of the temperate species. I revised the profile as follows (and removed the photo!). As you can see, it is indeed very invasive.
There are other plants very similar in appearance that may be confused with Limnobium laevigatum. L. spongia is a native North American Frogbit, and Hydrocharis morsus-ranae is a European/Asian plant sometimes referred to as Common or European Frogbit. This latter is a very invasive plant that was intentionally introduced into North America via Ottawa, Canada in 1932. It has since spread quickly and by 2003 was known to occur throughout much of southeastern Ontario, southern Quebec, northern New York and Vermont and eastern Michigan. "Frogbit" is classified in several states including California and Washington as a noxious weed. It is likely that some aquarium plants are in fact not L. laevigatum but one of the other two.