What should I do after multiple imputation in the data? I have a data set with missing observations. I used VIM package in R for imputation.
After imputation, I will try to run a hedonic regression.
Is there something I should do before going in to regression analysis, such as normality test?
 A: After multiple imputation, you fit a model to each of the imputed data sets, then you pool the results of all of these models together for inference. 
Since you mention you intend to use regression analysis, you can easily do this with the package mice (I don't know about VIM). See for example the accompanying paper, section 5.3. You may also want to inspect the quality of your imputations (same paper, section 4.5), but I assume this is what you used VIM for.
This is completely unrelated to any other model assumptions you might diagnose, as these depend on the kind of model you're fitting, rather than the imputations. You could extract the residuals from some of your models and perform the necessary diagnostics to check for violations, but the model you intend to use should already be substantiated from the type of data you're modelling. Also, beware of the dangers of formally testing for assumptions.
For example, before checking for normality of the residuals, is it reasonable to assume that the data-generating process for (what I assume are) housing prices has normally distributed errors? (HINT: housing prices cannot be negative and show much larger discrepancies at higher values than at lower values).
