I plan to buy a pre-owned hatch back automatic transmission car. What are the things which I should check before making the deal? Also should I go to the Company owned showroom and ask them to give me a report of the car health?
Most automotive shops can do a full inspection for $100-$140, have one done before you buy the car. If you are checking the car yourself, the main things you need to worry about are the engine (compression test, $15 tool), the transmission (rough shifts while driving), is the car driving straight on a flat road (alignment), is the AC blowing cold air (turn it on and wait a few minutes), is the battery holding a decent charge (12.6V with the car off, $15 multimeter set to 20VDC with the probes at the battery terminals), is the alternator providing a charge (14V with the car on and all accessories off, at least 13V with headlights, heater and rear defrost on, same tool and procedure as the battery test, yes you test the alternator by measuring the battery).
These are the things that could cause the car to break down unexpectedly.
In addition to tlhIngan's answer;
Get the VIN number of the car you're looking at, and get the vehicle history report. Compare it with anything the owner tells you.
Find out how long the previous owner has had the car - longer is better, and if they've owned it less than 6 months, be even more thorough on your checks - they may be trying to offload a lemon.
Look at the local area that your buying the car from, and the people you're buying from. if you don't feel comfortable, walk away. Honest people sell honest cars.
If you don't feel confident checking the mechanicals, ask for an inspection to be made. At least, get an MOT / Safety Inspection done before buying.