According to the dictionary definitions I found for DON'T ASK / DON'T ASK ME:
don't ask - is used to tell a person that the answer is so depressing one wouldn't even want to hear it: How am I? Don't ask.
don't ask me - is used to tell smb. that one does not know the answer: She's decided to dye her hair bright green, don't ask me why.
Does it follow the the expressions in question are NOT interchangeable in their respective contexts?