But the survey also measured what types of assets New Zealanders owned, and their support or opposition to the new tax.
That showed much higher levels of opposition.
"Turkeys don't vote for Christmas," said Horizon Research Principal Graeme Colman.
Among those with shares in companies, for example, 56 per cent were opposed.
Among those with residential rental or investment properties without a mortgage 66 per cent were opposed.
Of those with a residential rental or investment property with a mortgage, 74 per cent were opposed.
The strongest level of opposition by asset class was for those owning farms or lifestyle blocks in excess of 1ha, where 90 per cent were opposed.
Another thing which might worry the Government was that even among those who own their own home - which will not be subject to the CGT - there was stronger opposition, Colman said.
"Which suggests that message hasn't got through," he said.
Opposition to the CGT was extremely high among voters for National (62 per cent oppose, 23 per cent support) and ACT (86 per cent opposed and zero in support).
Of more concern for the Coalition Government was the higher levels of opposition among New Zealand First (NZF) voters, Colman said.
Among NZF voters, 55 per cent oppose, 30 per cent support, while 15 per cent are neutral.
That indicated the strength of sentiment the governing coalition would need to manage if NZF is to support some form of tax change, Colman said
The CGT was supported by Green Party voters (75 per cent for,14 per cent against), Labour voters (60 per cent for,14 per cent against).
Respondents were then asked if they would support or oppose the introduction of a capital gains tax.
They were also asked to say which assets they owned and were presented with an asset list.
The poll had 1116 respondents aged 18 or over and was undertaken between February 27 and March 15, 2019.
Results were weighted to ensure the sample represents the New Zealand adult population at the 2013 census.
At a 95 per cent confidence level, the maximum margin of error was plus or minus 2.9 per cent.
The survey was not commissioned by anyone and was conducted by Horizon Research in the public interest, Coleman said.