Can I do my tax returns for free?

Of Course You can, In case you are an individual and you are not required to get Audit of your Accounts.

But lets think it from different perspective. Like if you don't have complete knowledge of tax laws and still you file return on your own to save few bucks. You are definitely going to receive income tax notice for some errors or they even open scrutiny of your Accounts for past 3 years also.

So in my opinion you should let your CA to file your returns.