It would match the % required to pass the referendum. So if 65% is required, for example, and it seems like 65% might support it, then you should find out. What % is required to pass a binding referendum in the UK? What was required to determine the will of the people for Brexit?

You could do it for example like so: First you give volunteers limited time to collect a relatively small number of signatures, say about 1% of the voters in half a year, to start the process. If that is successful you transfer responsibility to the government and have the government determine whether at least 20% of the population is interested. If so, you hold the referendum.