Sources connected with the Heath Ledger investigation say the Drug Enforcement Administration set a new low for starf**king.

People who have talked to TMZ off the record are now willing to go on record -- still anonymously -- about one of the most bizarre DEA power grabs ever.

How's this for starters ... no one we've spoken with connected with the case can point to a single DEA case where a massive investigation was launched over an accidental death in which no criminality was even hinted at.

We know the DEA went all over the country, in one case tracking down a guy in California who smoked a joint with Ledger in the '90s, telling him he had to testify in a Grand Jury probe. And how's this for chutzpah ... the DEA told the guy he would have to pay his own way to NYC to testify before the Grand Jury!

In another case, the DEA was nosing around a film set in Arizona looking for people who had information about possible Ledger drug connections.

We know the NYPD was furious at the DEA for making an immediate power grab to control what should have been a simple case. NYPD cops felt "humiliated" by what one source called "utter disrespect" on the part of the DEA.