Launch App Store and click on the 'Purchased' tab. If you have iMovie associated with your Apple ID it will appear in the list and show a button which will say:
'Open' (if it is already installed) OR 'Install' (if you have bought but not downloaded it or have deleted it)
It is safe to delete it if it appears on the list. If it does not it means that the app on your computer is associated with another person's Apple ID. In that case you will not be able to re-download it for free under your Apple ID.
Geoff.