Mutual Funds

You can invest in mutual funds without any restrictions (except for US & Canada based NRIs*). As a first step, you should update your KYC as an NRI investor. If you are already an investor, you have to change your KYC with NRI status. If you are new to mutual funds, you can submit the following documents at the office of any fund house or registrars like CAMS or Karvy for KYC. They will verify your documents and do the in person Verification (IPV). You can do this during your visit to India or before leaving India. As an NRI, you can invest in mutual funds on non-repatriable basis or on repatriable basis. If it is non-repatriable basis, you can invest from NRO account. Otherwise you have to use NRE account.

AMC's like PPFAS, UTI and a few others now allow US and Canada based NRIs to invest in mutual funds. Tax treatment on mutual fund redemption amount & dividends for NRIs. The taxation of mutual fund for NRIs is similar to resident Indians. But there are TDS for NRIs.

Equity Funds

If you sell equity funds after holding it for 1 year, the gains are treated as long-term capital gain and it is tax-free.  But, if you sell it within 1 year, the gains are treated as short term and it is taxed at 15%. For NRIs, there is TDS of 15% in this case.