The Medical Certificate of Causes of Death has a section (near the end of the form) for listing any "infectious disease."
- "If the deceased was at the time of death suffering from an infectious disease, whether or not covered above, name the disease."

This refers to diseases that should be notified to the Medical Officer of Health and that could possibly be a risk to funeral directors, embalmers or grieving whanau who touch the body after death.
It does not refer to infections in general (for example "pneumonia" or "cellulitis")
Funeral Directors are expected to handle all bodies with basic precautions against infectious diseases, if only because deceased patients (as with live patients) may be carrying infectious diseases without anyone else being aware of it.

The Ministry of Health has guidance about completing this section: infectious diseases.

Quoting that advice:

Below the section Cause of death Part 2 on the Medical Certificate of Cause of Death is a field requesting information about any infectious disease the deceased may have been suffering from at the time of death.
This is to assist the funeral director to meet reporting obligations set out in section 85 of the Health Act 1956 and its Regulations.
The infectious diseases to be reported on in certain circumstances under the Health Act 1956 are listed in Parts 1 and 2 of Schedule 1 of this Act.
Providing this information also makes the funeral director and other professionals aware of the infection so they can take the necessary precautions to keep themselves safe when handling the body.

List of Notifiable Infectious Diseases published in Schedules 1 and 2 of the Health Act as at May 2018: List