The woman and her daughter retain name suppression.
The court earlier heard how Gottermeyer had been suffering from a significant depressive illness.
Justice Fogarty jailed Gottermeyer for life yesterday but adjourned the case until February 28 for a psychiatrist's report under section 104 of the Criminal Procedures (Mentally Impaired Persons) Act to be prepared to establish his mental state of mind at the time of the killing.
He will then determine the length of the minimum non-parole period.
The judge asked for the report to include notes on why Gottermeyer was still on medication, why he was at outpatient at Hillmorton when the murder occurred, and any other clinical observations which would assist the court in judging "to what extent his history of depression and associated episodes" contributed.
The Canterbury District Health Board said an investigation would be carried out. A spokeswoman said the case and any recommendations would be reported in the Health Quality and Safety Commission's annual report.