There are 95,580 registered voters in Tauranga.
All votes must have been received by the council by midday on Tuesday for both the referendum and the byelection.
Electoral officer Warwick Lampp, of Electionz, said preliminary results will be announced mid-afternoon that day.
He said it was probably too late for people to send in their votes by post.
"You can drop them off at ballot boxes at libraries and at the main council office, and for the referendum, you can vote online."
He was expecting a late surge of votes that he predicted would take the total participation rate to around 30 per cent, which he said was at the higher end for a by-election.
Lampp said the online voting option in the museum referendum was the reason participation was higher in the referendum than in the by-election.
"It shows that people have an appetite for voting in an easy and convenient way."
The referendum was an online voting first among New Zealand councils and will be viewed as a test case for the security and accessibility of the technology.
Just over 3500 people had cast their referendum votes online and Lampp said he was very happy with how it was going.
"There have been no hassles or security concerns."
The number of voting packs returned because the person was no longer at that address was sitting at just over 1000, about 1 per cent of the total voters, which was about normal.
Tauranga mayor Greg Brownless said the participation level was "a little bit disappointing".
"I thought we might have a bit more interest with the combination of the referendum and the chance to have a say in electing another councillor.
"It certainly excited a lot of people to put their hands up and run, and I thought that might have translated into more people voting.
"It would be good if in the last few days lots more people can get their votes in."
Brownless said that with 20 candidates running it was "anyone's guess" who the winner would be.
"I honestly have no idea."
Electoral returns
By-election
Votes counted - 22,221
Per cent of registered voters - 23.25%
Museum referendum
Postal votes - 20,442
Online votes - 3589
Total votes counted - 24,031
Per cent of registered voters - 25.14%
Total registered voters - 95,580
- Source: Electionz