It is also claimed boos were heard when “No” votes were opened at the Highland and Islands count in Dingwall.
It is believed complaints were made by members of the Lib Dems and Labour who were acting as official monitors.
Highland Council has confirmed it received complaints during the count.
A spokesperson for the Highland Counting Officer said: “Complaints were made about a count staff team of four people at the referendum count in Dingwall and as a result the team were stood down and replaced.”
The local authority declined to comment on whether they would be disciplined further.
Highland Council said replacing the staff did not contribute to a delay in the count.
The result from the Highland area was the last in Scotland to be declared after almost 30 ballot boxes were delayed by a fatal crash on the A9.
A lorry driver died when his vehicle crashed near Berriedale Braes in Caithness on 18 September.
Twenty-eight boxes were driven by a long diversion via Melvich on the north Sutherland coast.