I created a new store in shopify. I was able to import the products and add the collections by hand. Is is possible to assign products to collections using csv? I have around 3500 products. Any help would be much appreciated.
I don't think you can. Due to the way collections can be built (manually or based on criteria), they skip that altogether.
It is possible to create collections with the Shopify API, but again, due to the nature of how they work under the hood, it is not easy to allocate a large number of products to a collection without some real fine-grained control, making an App or script tough to write.
You best bet might be to write some scripts to at least populate your most basic collections with products, and then create the missing ones with your Shop admin.