Can I open a New PPF Account in April 2016. I have been living in US and also in India for last few years

Firstly, to open a PPF account you need to be a resident Indian. Non resident Indians cannot open PPF accounts. The question therefore, is whether you are a resident Indian? Under Section 6 of Income Tax Act, an individual will be treated as a resident in India in any previous year if he fulfills any of the following two conditions:

(a) He/she is in India in that year for period or periods amounting in all to 182 days or more, or

(b) Having within the four years preceding that year been in India for a period or periods amounting in all to 365 days or more, and has been in India for 60 days or more in that year.

You can determine whether you are a resident Indian or NRI based on the date stamps on your passport. Based on the information provided in your query, it seems that you are a resident Indian, but you should consult a Chartered Accountant and provide your passport details, to seek his advice on whether you are resident or non-resident.