In general, sure, you can (barring the Bag of Rats situation).
Where, if anywhere, does it say that you can or can not hit yourself with a melee basic attack. Same with a targeted burst?
This comes up occasionally with the dominate status, the hypnotism power and similar.
As far as I am aware, Dominated creates only get access to your At-Will Powers and these can be used against any creature, often an ally. Suggesting that you would never attack an ally expands to the you would never attack yourself.
I think it is only previous editions (pre 4e) that allow a Saving Throw if attacking ones self, so i think it is entirely possible although I would recommend that any DM presented with this decide for themselves since it wouldn't break the game if it went one way or another.
Such rules could include
a) A saving throw allowed immediately before the attempt
b) A cumulative bonus to future saving throws
c) A saving throw allowed to ignore the attempt only, if successful then still dominated and the creature can not attempt to do it again this turn but gets another try and another action
As far as I am aware, Dominated creates only get access to your At-Will Powers and these can be used against any creature, often an ally. Suggesting that you would never attack an ally expands to the you would never attack yourself.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.