The man took the officers into his apartment and showed them the medication, at which point his partner and children arrived home.
His partner was very upset that police were there, and subsequently one of the officers decided to arrest the man, "partly so that he and his partner would be separated for the night to 'cool off'", the IPCA report said.
The man became upset at the thought of leaving because his young son has cancer and they were only in Auckland so his son could be treated at Starship Hospital, according to police.
He said that he needed to administer medication to his son twice a day.
The man decided to flee from the officers to avoid being arrested.
He jumped over the apartment balcony's railing on to the concrete about 4m below, and broke his ankle as he landed.
Unaware that the man had broken his ankle, the arresting officer fired his Taser at him twice. The first firing missed but the second connected.
The IPCA determined the officer had no lawful justification for using the Taser to carry out the arrest or prevent the man's escape.
"The [IPCA] is not satisfied the officer fired the Taser to defend himself or others, because the man had just run away from the officers and his partner, removing any imminent threat the officer believed he posed to them," said IPCA chair Judge Colin Doherty.
"Nor did the man pose an immediate danger to anyone else after he jumped from the balcony.
"Additionally, the officer was not justified in using the Taser to prevent the man's escape."
The IPCA also found while the officer had legal justification for arresting the man, it was not necessary.
"If the officers were concerned about leaving the man and his partner together, they could have further explored the availability of other options for separating them which enabled the man to provide his son with the medication he needed on schedule."
Auckland City District Commander Superintendent Karyn Malthus said the officer had made the wrong call.
"Police completely accept the findings that Officer A should not have tasered the man.
"While the situation was not helped by the man deciding to flee arrest, I would also have preferred it if the officer had given more thought to the stressors evident in the family and to recognising the parents' concerns for their ill child's needs."
The officer involved had been given further training following the incident.