Final answer:
A user with profile level CR permissions and OWD set to Private can create new contact records and read their own or shared contacts but cannot access other users' contact records without additional sharing permissions.
Step-by-step explanation:
When a user has profile level CR permissions on a contact object and the Organization-Wide Defaults (OWD) are set to Private, the user is limited in what actions they can take. Specifically, the CR permissions imply the ability to Create (C) and Read (R) contact records. In Salesforce or similar systems, this would mean the user can add new contacts and view existing ones that they own or are shared with them. However, since the OWD is set to Private, they cannot view or interact with contact records owned by other users unless specific sharing rules are in place or manual sharing is performed by the record owner.