The citizenship of any country has nothing to do with tax liability applicability in India. You may have passport of India or any other country still may be liable to pay taxes in India.

For Indian income tax purposes, if you are USA citizen, assuming you only visit India only for vacations, you still are liable to pay tax on Income generated in India I.e You are settled in USA for a long period of time and are now selling your or your inherited property here in India and wish to repatriate the funds back to the USA. In this case, since Capital Gains would arise in India, you need to pay taxes in India before you move out the money. Of course, there is a Double Taxation Avoidance Agreement of India with USA. Thus, you wouldn't have to pay tax twice (once in India and once in the USA) on the same income.

You may also read more about Residential status, ROR (Resident and Ordinarily Resident), RNOR (Resident and Not Ordinarily Resident), NR (Non Resident) on the Central Board of Direct Taxes, Government of India