if a district attorney drops charges agianst you, then is pressured by a political person can they open the investigation again
If the charges were simply dropped by the State without being dismissed with prejudice by the court they can re-open the investigation.
Though there are exceptions, generally a criminal charge that has been dismissed by a prosecutor, can be refiled and again prosecuted, within the stattue of limitations period. (The shortest Minnesota statute of limitations is three years.)
Charges may be refiled if the original case was dismissed by the prosecutor without prejudice.