Is there scientific evidence connecting the current climate in India with global warming?
If you look at this link - Climate Of India there are four seasons affecting different regions of India 

1) Pre monsoon showers 2) Indian Summer Monsoon 3) Post monsoonal rain. 4) Winter rain

Each of them have their own patterns and dynamics. From the perspective of the second and biggest impact on the country i.e. Indian Summer Monsoon it would be hard to find a single year where rainfall distribution has been completely well distributed i.e. all regions of the country had experienced surplus rainfall. But this unequal distribution would be made up in subsequent years mitigating drought. Or so it was thought. 

For the monsoon to bring bountiful rainfall oceans must remain cool(relative to landmass) and land must warm during the crucial months of April and May. But this recent study published in Nature shows that there has been a  weakening of the land sea thermal gradient and drying up of Indian subcontinent/Drying up of Indian subcontinent due to weakening land sea thermal gradient. So according to that paper human influenced climate change causes the Indian  landmass to cool because increasing concentration of  aerosols suppress the surface warming.

Secondly there is an asymmetry in the El Nino forcing.


  Meanwhile, a recent study demonstrates that apart from the warming due to greenhouse gas forcing, the long-term warming trend in the western Indian Ocean is significantly associated with the asymmetry in the ENSO forcing. That is, while the quasi-periodic El Niño events induce a warming over the Indian Ocean via the Walker circulation, the La Niña events fail to do the inverse. Along with this, an increase in the magnitude and frequency of El Niños in the recent decades has accelerated this warming. The heat pile-up due to this ENSO forcing persists in the land-locked Indian Ocean that has a restricted thermohaline circulation, sustained by a feedback from the local air-sea interaction and ocean dynamics.


What this means is that the traditional monsoon dynamics i.e. cool Indian ocean and warm continental land mass has been disturbed by human influenced climate change as well as the natural geography of the land and ocean mass. One significant ISM phenomenon the tropical easterly jet stream has shown a  weakening trend over the last few decades. A significant fall out of this could be mid latitude atmospheric dynamics could come into play during the ISM(one can think of this as the weather during a break in monsoons where upper level subtropical westerlies come into play) and a disturbing trend has been noted in recent times with increasing frequency of hail storms.