CA's Head of Integrity Iain Roy and team performance manager Pat Howard travelled to South Africa to begin interviews with Smith, Warner, Bancroft and coach Darren Lehmann.
Roy will then decide how players are charged under CA's code of behaviour.
According to ESPN Cricinfo, if Roy hands down a charge of conduct contrary to the spirit of the game, an independent commissioner would then be brought in to give a ruling.
The maximum penalty available is a life ban.
The ICC ruling for Bancroft means he'll be free to take part in the fourth and final Test of the series, pending Cricket Australia's investigation.
According to the ICC rule books, ball tampering is a level 2 offence and carries up to four demerit points (automatic one match suspension) and up to 100 per cent match fee fine.
There was widespread condemnation for the soft ICC decision.