This is the list of documents you need to apply for the residency permit:
1. Proof of ownership of the property (List nepokretnosti) that is not older than 6 months
2. Proof of a 3.650 EUR deposit into a bank in Montenegro
3. Valid medical insurance for a period of not less than 30 days
4. Copies of each page of a valid passport
5. Certificate of no criminal record from the country of origin (not older than 6 months and officially translated).
Also, within 24 hours of your arrival in Montenegro you need to register your arrival with the local police branch or with the closest tourist office (turisticka organizacija). You will need to be registered there in order to receive the permit.