A Coroner has decided against opening an inquiry into the death of Christchurch school girl who fell and hit her head on a school ice skating trip

13-year-old Kymani Hiley-Hetaraka wasn't wearing an optional helmet when she fell and fatally hit her head on ice, at Alpine Ice Sports Centre last year.

Alpine Ice has since made helmets mandatory, and the school has overhauled risk management and safety processes.

Coroner Alexandra Cunninghame says a WorkSafe investigation found no breaches of laws, and concluded no further action was needed.

The girl's mother has told the Herald the family is angry, because they want those responsible to face consequences.

But the coroner says the family agreed, through their lawyers, that an inquest was not necessary.