The 39-year-old was caught with the plant on February 4 this year.
The charge carries a maximum penalty of three months in jail or a $500 fine. However, as a first time offender, he was offered the chance to avoid conviction.
Court records showed a registrar dismissed the charge on April 30 after confirmation Tepania had successfully completed police diversion.
The dismissal of the charge means no criminal conviction will be entered under his name.
Diversion provides predominantly first time offenders with the opportunity to avoid conviction for what the police deem low-level offending.
It involves a defendant accepting full responsibility for their crime and agreeing to fulfil certain conditions in exchange for the charges being withdrawn.
The NZ Teachers Council has referred his case to its Complaints Assessment Committee (CAC) for investigation.
NZTC spokeswoman MaryRose Painter said that, since the committee's investigation was private, no further details would be revealed.
"CAC are able to remove a teacher from the classroom while they investigate if there is sufficient concern for student safety. However, they have concluded that is not necessary in this case," she said.
Tepania's teaching certificate is still valid and will expire on August 3 this year.
Part of the committee's role is to assess whether Tepania should be permitted to continue to practise while any court or council investigation proceeded.
Information released by the New Zealand Teachers Council under the Official Information Act showed 35 teachers in Northland were reported to the council for conduct and competence issues in 2014. Seven of those teachers were convicted for offences such as dishonesty or drugs.