Yes you are eligible. But to know in detail the eligibility, check the criteria below:

This is the first step if you have not done yet:

'Candidates must get re-validated his/her registration to Common Proficiency Course in case it has been three years since their CPT registration. Candidates must note that CPT course registration is valid only for three years. So, candidates who are already registered need to re-validate from concerned Regional Office before their registration expires before three years.'

If you have met the above eligibility then you can apply for the CPT test.

Go through the complete criteria here.

You have a government organisation experience that is good.

You can appear for CPT, if you make it then go ahead with your interest and if you could not by chance, then you have experience in your hand so you lose no where.

Good Luck.