Yes, Ideally all integration is done using industry standard communication protocols, requiring some middleware that links these standards. Ideally these protocols would be something like a webservice as you say where the API ensures validation all data imported into your system.
Most basic integration between systems means Transfer of Data between systems. You can either choose to build an API to which you or others provide the middleware to connect. Or depending on the nature of the applications, you your case CRM, it may be worth ising this same API to build an Import/Export mechanism where users can just just Export their data into xml, CSV and also import their data, building a nice interace to map any CSV format to your own fields is a nice touch and means less technical users can perform non-automated tasks.