The NZFS investigated the claims made about Ms McHugh and on January 28, 2014, Ms McHugh was given an oral warning.
Until receiving the oral warning Ms McHugh had a blemish-free record.
Authority member Vicki Campbell found the NZFS hadn't conducted a "full and fair" investigation in to the claims of bullying.
"There was more NZFS could have done," she said in her decision.
Ms McHugh told the authority that the warning was inconsistent with other warnings issued in the past, and Ms Campbell agreed.
Ms McHugh was seeking $35,000 in compensation for the warning, but the authority awarded her $5250.
The authority said Ms McHugh hadn't fully upheld her duty to act in good faith to her employer when she secretly recorded a meeting and didn't tell her employer.
But, Ms Campbell said Ms McHugh was disadvantaged by the warning and was overlooked for a transfer to Tauranga because of the mark on her record.