(Just a heads-up, the Eurozone and the EU are different – the former is the currency union under the Euro, and membership of the latter is what the referendum is about. Not all members of the EU are members of the Eurozone).
Scotland had an independence referendum less than two years ago, where the outcome was a good 45%-55% in favour of remaining in the UK. However, the majority of representatives in Scotland remain pro-Scottish independence. Continued membership of the EU was an important argument during the independence campaign – with the pro-independence side wanting to remain, and the pro-UK side warning that Scotland would lose EU membership if it voted for independence.
It's likely – but not certain – that there would be a second independence referendum in Scotland on the basis of being 'forced' to exit the EU. But it's not going to be pretty, and there have been a lot of elections in Scotland recently – no doubt everyone is getting a bit fatigued. It's not clear at all what the outcome would be, either, or if Scotland would even be able to maintain EU membership.