Can I assign a follow-up for a particular contact in CashManager? 

Yes you can. You will have to first enable the 'Contact Management' feature in CashManager which can be activated from Setup>Options>Features and select 'Activate Contact Management feature', Also select 'Show due tasks' if you want to.

Once the Contact Manager feature is enabled click on the 'Contacts' button, select a particular contact and click the 'Notes' button. This will give you an option to insert a reminder in the form of a note which will be shown under due tasks on the due date.