Chris Brown Accused of Pulling a Road Runner

Chris Brown got served with a court summons, but bolted at top speed when he saw the papers ... so says the process server.

According to new legal docs ... CB was in a charity basketball tourney on September 11, and the server went to deliver the summons. This was the same game where Chris refused to stand for the national anthem, and beefed with security.

The server says she approached Chris at halftime ... pulled the docs out of her bag, and said the magic words -- you've been served. She claims Chris totally saw her, but a member of his entourage slapped the papers to the ground.

She says they landed at CB's feet, momentarily, before he went all Usain Bolt in the opposite direction.

Brown was being served over claims he beat the hell out of his former manager, Mike G.