Breaking ties: drawing lots, tossing a coin, hand of poker?

The DomPost is reporting that the Wellington mayoralty might be settled by a coin toss:

COIN TOSS COULD SETTLE WELLINGTON MAYORALTY
Wellington's mayoral race could be decided by a coin toss.
But the pendulum may be swinging back in Kerry Prendergast's favour, with nearly 200 of the special votes that will decide the city's knife-edge election being discounted.
Election officials sorting through hundreds of special votes say that, in the event of a tie, names could be drawn from a hat or a coin could be tossed, under police supervision.
"We'd obviously get legal advice on this, but my understanding is that it would be determined by lot," electoral officer Ross Bly said. ...

A great story, but – in this case – wrong. I hope Bly seeks legal advice on the point.
Bly is partly right though. The usual practice with first-past-the-post local elections is for ties to be resolved by the drawing of lots. Regulation 58(5) of the Local Electoral Regulations 2001 provides:

(5) If, in acting under subclause (3), there is an equality of votes between candidates and the addition of 1 vote would entitle any of those candidates to be declared elected, the electoral officer must determine by lot which candidate is to be declared elected.

There is the live question of what "determine by lot" means in this context. I don't think it includes tossing a coin, although given the randomness of the method, I doubt it would be challenged. Drawing marked pieces of paper or playing cards are common methods I understand.
As an aside, I am told that in Texas the prescribed method is playing a hand of poker! (Bonus points if someone validates this and forwards the legislative provision.)
But, in the case of the Wellington mayoralty, the election is conducted under STV and there is no direct equivalent to regulation 58(5). Instead, I understand, the certified counting programme makes provision for resolution of ties through the generation of a random number. Clause 34 of Schedule 1 to the Local Electoral Regulations 2001 provides:

Ties
cl 34 This clause applies if—
(a) a candidate with the lowest number of votes is to be excluded but 2 or more candidates share the lowest number of votes; or
(b) a candidate whose votes equal or exceed the absolute majority of votes is to be elected but 2 candidates' votes equal the absolute majority of votes.
If this clause applies, in the case of (a), exclude the candidate identified by the AAFD method as the candidate to exclude. If the AAFD method does not identify a candidate to exclude, exclude the candidate with the lowest PRN. In case of (b), the candidate who is not excluded is elected.

The regulations define PRN as "the pseudo-random number generated by the PRNG method" – a method which is described in the regulations.
So, yes, a tied vote for the mayoralty might be resolved randomly. But, no, it won't be through the toss of a coin (as exciting as that would be!)