Masters degree through distance while working in government job

For continuing your education through distance mode you need not take the permission of the current employer. That is OK. But the institute which gives admission to you into the course may ask for proof of employment and then you have to take a certificate from the employer and submit it. Otherwise, the institute may not accept your application. In such a case, you have to inform your employer.
You are working in a state government department. Your employment will be covered by certain rules and regulations. You have to follow all those rules and regulations. Otherwise, you will be disqualified. So please review those terms and conditions and see whether there is any special mention about your continuing education. If there is anything under that clause, you should follow that without fail.

You will have to go through the model standing order of your organisation where you could notice the details of the regulations to be followed during your service period. You have to show your courtesy if indulged in some activities other than doing your job in the government sector.
Any breach of the rules of the standing orders would seriously be reviewed and any negligence of the such rules on your part would reflect your gross misconduct.
It is only because of your job condition in the government sector, you need to intimate your present employer regarding your perusal of studies though it may be of distance mode as indicated by you of choosing Geography for your studies further.
Don't take a risk by inviting a legal issue which could cost you substantially in future.

In every Govt. organizations or Department there is a scope to updated the academic as well as practical qualifications with your career data base. In some department you can get an extra increment by adding any upper qualifications. Additional qualification also benefited you for promotion in next higher grade. Therefor while doing any such event you need to made an application through proper channel to the Administrative HOD. In the application you must indicate that for your future career growth it is required to do Master degree through distant education mode and no leave is required for obtaining the degree except at the time of examination. The application must be submitted prior to taking admission. Your office after taking competent approval will issue an office order indicating approval for acquiring Master degree through distant mode from the college/Institute without any guaranteed benefits or leave from this office except leave may be granted for examination purpose.
After applying you can take admission. I think as a Govt. Office you should take prior approval for getting benefits.

You can get your Masters Degree without taking any study leave given that you can effectively manage your career as well as education. But you have to provide the necessary information regarding your employment in the institution you are getting a degree from. Studying more and more is always welcome as all the sectors are looking for highly qualified employees be it private sector or public sector. Many Online Distant Learning Organizations like IGNOU have a huge number of courses available at reasonable prices. Many Jobs provide scopes in increment after adding more qualifications. But as you are working for the State government, I would recommend that you inform the authorities and take all the necessary permissions required in order to continue without any barriers. I do not think there is much of a hassle to go through for this as education has always been a top priority for the country.

Also Good Luck and I pray that everyone who see this can manage their jobs as well their education efficiently.