Take a simple course and prepare hard for UPSC. BA History would be an added advantage for preparation. But Incase you don't crack UPSC you won't be having any back up for your career. Few of my Engineering friends has very good percentage in Engineering and preparing for UPSC. Engineering is their back up

You can consider below given eligibility criteria for the same -

To be with Indian police you have to appear for the Indian Police Service Exam conducted by the UPSC. IPS is for the recruitment of the top ranked police officials to be posted all across India.The minimum eligibility for IPS exam is that the candidate should meet the physical and other requirements as mandated. Minimum age should be 21 years and maximum age should be 30 years. Minimum educational qualification should be a bachelors degree in any discipline or an equivalent qualification from recognized institution. Minimum height is 165 cm for Men and 150 cm for Women (minimum height is relaxed by 5 cms for Men and Women respectively for reserved candidates. Minimum Chest girth fully expanded is 84 cm for Men and 79 cm for Women. Expansion of 5 cm for Men and Women.
You can appear for the written test conducted by the respective state PSC to get jobs with the state police.

Hope this helps!!!