I am not aware of your industry. In my opinion, if you have hired a person as a contract employee on a retainership basis for a specific period by signing the contract, then there is no need to have a separate appointment letter. The terms and conditions remain similar in the contract as per the appointment letter. This approach can be utilized for highly qualified/technical persons only. Do not adopt this practice for workmen or clerical staff categories. Otherwise, you will run into trouble under the Contract Labour Abolition Act and the ID Act regarding their permanency.
If you are hiring a person through a contractor, then there is no need to have a separate contract or appointment letter for each person.