To conduct water balance, we often refer to the water year ends (ceases) with usually the least streamflow.  From your data and Dr. Towe's summary, the driest month on average is July, so you could pick end of July as cessation as a logical choice.  However, August is almost as dry, and my guess is often the month of extreme low flows, so picking end of August as cessation of water year may be best.  If you have some streams gauged for long term flow, this could be checked.  In USA, we use October 1 to September 30 as our water year.  We often also report data by calendar year, as some prefer to report that way. 

If conducting research, it would be best to be consistent with other researchers in your country recognizing your climactic conditions and utility of the data for your needs.  There is no reason why you cannot calculate and report more than one way, but recognize if inconsistent with the norms, you may still find it necessary to report to the other standard(s).

in addition of Towe & Hansen's opinion:-

Looking to the mean rainfall recorded during the three consecutive months (i.e., JFM= January, February, March, AMJ= April, May, June, JAS= July, August, September, OND = October, November, December) it may be concluded that JAF and OND are main rainy season in your area. Because over the years, maximum rainfall occurred during these months. Interestingly after 2006, between October and December (OND) always highest rainfall was recorded than rest of the period. However before 2006, JFM season rainfall was frequently surpassing the OND. Hence, it is clear evidence of change in the rainfall pattern in your region. As for as periodical rainfall distribution is concerned, April to June (AMJ) can be reckoned as third whereas, JAS receive least rainfall (see attached figure).

These informations can be immensely useful in advance crop planning and in-season managements.

I would like to thank you Kenneth, William and Sudhir for helping. I know understand what is happening. I appreciate you quick response too.