State police Tuesday said they are not considering the death of Tafari Campbell, who was found in Edgartown Great Pond earlier this week, suspicious.

Mr. Campbell, 45, went missing Sunday while paddleboarding on the pond and divers recovered his body the following day. A post-mortem examination by the state medical examiner found no external trauma or injuries, police said in a statement.

Police interviewed another paddleboarder who was with Mr. Campbell Sunday and they indicated that Mr. Campbell was standing on his board, lost balance and fell into the water. Mr. Campbell struggled to stay afloat and then went under the surface.

Mr. Campbell, who worked as a personal chef for former President Barack Obama and was near his Edgartown summer home, was not wearing a personal flotation device and was not leashed to the paddleboard, police said.

The other paddleboarder tried to swim to Mr. Campbell, according to police, but was unable to reach him in time. The other man then swam to shore and told another person what had happened. That person called 911, which initiated a wide-ranging search that spanned Sunday night and Monday morning, according to police.

The investigation into Mr. Campbell’s death and his post-mortem examination are now completed, according to police, with the exception of toxicology reports. Running those tests are standard practice in all autopsies and generally take several weeks to complete.

“Barring any further significant developments, which are not expected at this time, the State Police will provide no further updates on Mr. Campbell’s tragic passing,” police said.