Venus Williams' phone records could be crucial in the wrongful death lawsuit filed against her ... or attorneys for the man who died in the accident think so, anyway.

According to docs, attorneys for Jerome Barson's estate have filed a request for documents from the tennis star. They want all bills for the month of the accident for any smartphones and devices Venus owns.

Sources connected to the case tell us Barson's team wants to make sure Venus was not talking, texting or using her phone in any way in the moments leading up to the June 9 accident win Palm Beach Gardens, FL.

In the surveillance video ... you can see Venus' left elbow resting on the door through an open window -- we've slowed it down, but it's still not clear if she's holding a phone.

The estate's attorney, Michael Steinger, is also requesting prescriptions for any medications Venus may have taken within 72 hours of the accident.

Police have already said drugs and alcohol did not play a role in the accident. They also say she was not distracted by her phone.