There are two ways to join as a CID officer:

• Join state police services and on promotions as instructed by your seniors you can be posted to the CID department. For this you will need just a graduation degree.
• If you want to join CID directly then its ideal to give the Indian Civil Service examination conducted by UPSC. On qualifying the exam i.e., in Prelims, Mains and Interview you can get the CID post. Also for this exam you will need to be a Graduate.

So in order to be a officer in CID you need to be just a graduate. So if you want you can go for LLB else, BA will be a great course with the preparation for UPSC side by side.

To know more about UPSC visit the link provided below:

https://competition.careers360.com/exams/upsc-civil-services-exam

I hope my answer helps. All the very best for your future endeavors!