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The pair were suspended on April 24 after returning positive tests for cannabis following the Nuggets' home match against the Taranaki Dynamos on March 28.
The Sports Tribunal of New Zealand, in conjunction with Drug Free Sport New Zealand, held an anti-doping violation hearing via teleconference on Tuesday evening.
The pair effectively admitted the charge after deciding not to have their B sample tested.
Otago Nuggets general manager Warrick Diack confirmed yesterday the players had been suspended until June 1, a six-week ban.
However, they would now undergo an internal investigation, with input from players, coaching staff, senior management and Basketball Otago's board.
"From Basketball Otago's perspective, we'll now evaluate each case on its merits and decide on the best course of disciplinary action for these players," Diack said.
"Even though the Sports Tribunal has suspended Nat and Steve, we'll now complete a full and and fair investigation internally. We hope to have it resolved this week," Diack said.
Diack was confident the incident was a one-off and that there was no drug culture within the Nuggets team or New Zealand basketball.
"In the past five years, there have been 416 drug tests completed in the NBL, with five positive tests returned in that period."
Asked if Connell and Robinson had placed their future playing contracts with the Nuggets in doubt, Diack said they would need to assess what the implications of bringing pair back next year would be.
"We have obligations to ourselves as well as the message we send to the community, the fans and the sponsors.
"From what we understand, a lot of the players were as surprised and disappointed as we were when we found out. Especially with Nat Connell, a starting point guard and captain of the team. It didn't send a very good message, to be honest."
While the players' suspension would end before the Nuggets final game of the season against Canterbury on June 7, Diack said any decision on the players' involvement in that match would not be made until after the internal investigation.