Initial setup of settlements
From the official game rules:


  The starting player places a settlement on an unoccupied intersection of his choice. He places a road adjacent to this settlement. The other players then follow clockwise. Everyone places 1 settlement and 1 adjoining road.
  
  Once all players have built their first settlement, the player who went last in the first round begins round two: he builds his second settlement and its adjacent road.


So no, a player may not place their second road adjacent to their previously-placed settlement, or the road leading from it, because the above rule explicitly instructs that the 2nd road is built adjacent to the 2nd settlement.