There are two sets of laws.. Now in most states a trailer under 2,000 pounds is NOT required to have aux brakes (Not necessarly electric) but may be so equipped.
Depending on the state however trailers as light as 1500 pounds may need brakes,, in other states 3999 pounds does not but 4K and up do.
(Moral your millage (Weight limit) may vary)
The other law is civil
Having brakes on the trailer can make a BIG difference in your skid distance. So if you are sitting there, steam coming off your busted radiator, And I'm in front of you with a dent in my truck.. You better hope your have brakes on your trailer. It's that simple.