Q: Hi Ben, there was no leakage before I went for an oil change. The service center replace a nut at the oil pan and its leaking oil

If you went to a service center, in all probability the work that they performed is covered under a warranty of some sort. Additionally, if you paid by credit card, for sure you are covered if you have encountered a problem that was caused by the service center (you would simply maintain documentation and dispute the charge with the credit card company).

If the oil pan drain plug was replaced at the service center, and if that plug is the source of the leak, either the drain plug is "loose" or the gasketing (if used) is not sealing well. If, to repair this, they have to remove the drain plug to either repair the threads, or add a gasket to the drain plug, all the engine oil will have to be drained out. It is not recommended to return that oil to the engine. To get a sense of "who" you are dealing with, in the event that this is a drain plug issue, ask them what value they set the torque wrench to to tighten the drain plug. It will vary from car model to car model but in your case, according to the instructions, it is probably around 18 ft. lbs. (216 in. lbs.). Upon asking that, if they look at you like they never heard of a torque wrench, or it is obvious to you that they do not use such a tool, run for the exits (figuratively, get it repaired there because it will be no additional cost to you but do not deal with amateurs). You can get an oil change less expensively through YourMechanic and the drain plug will actually be tightened to the right amount using the right tool.

With regard to your very specific question as to whether you should repair it yourself, you could attempt it but you might have a circumstance where the drain plug hole has to be re-threaded, or a thread insert placed. Or, it could just be a missing gasket. Also, you have the issue of who pays for the new oil. Assuming they don’t do further damage, the cheapest option is to have them fix it and they assume these costs. If you desire that a professional look at it, simply request a leak inspection. If you have further concerns, by all means please follow-up and we will be glad to help you.