Comparing two overlapping samples in a tracking study

#1
I have a quick query about measures of sample accuracy in a tracking study with an overlapping (common) sample, and couldn't see anything here already. Perhaps it's a new one!

I have a large tracking study with a sample size of n=3,600 . The confidence interval for each track is therefore max. +/-1.6% at the 95% confidence level. That much I am clear on!

I think that in the normal scheme of things when I am comparing this year's sample with last year's I should simply double that (to +/-3.2%) because each distinct sample size has that margin of error. That would mean any movements over +/-3.2% are significant.

However, there is a complicating factor in that half of each of the samples is common, i.e. n=1,800 respondents who responded last year also responded this year. We did this so that we could ask them 'why they changed'.

Given this I am wondering what the impact on the confidence interval is when comparing the samples / trend or even if I am using the correct measure)?

I understand that each sample will have results +/-1.6% confidence interval for that point in time, but given the shared sample of respondents I think that the comparative margin of error will be lower than +/-3.2% as they are 'real changes' over time amongst the same sample of people?

In fact, I am guessing that the +/-3.2% would be halved when comparing movements between the two samples, i.e. that movements over +/-1.6% are significant. Is that right?

Any help you are able to provide in answering this question would be gratefully received!