# Does the difference in difference techniques assumes the dependent variable has a normal distribution?

I'm trying to estimate the effect of an event. The data I have is number of sales in 7 different periods of time (3 periods before the event, the period that the event happens and 3 periods after the event). I have a relatively small group to that participate the event and a much bigger that didn't with similar characteristics. When we performing a difference in difference we generate a control group dummy $$treat_{i}$$ which is equal to 1 if a person is in group A and 0 otherwise, then we generate a time dummy $$time_{t}$$ which is equal to 1 if t=2 and 0 otherwise, and then we regress:

$$Y_{it} = \beta_{1} + \beta_{2}(treat_{i}) + \beta_{3}(time_{t}) + \rho (treat_{i} \cdot time_{t}) + \epsilon_{it}$$

So my questions are:

1. Do we assume $$Y_{it}$$ have a normal distribution?
2. Should I use a grouped variable such as mean or median for $$Y_{it}$$ over time or the whole data?