You would have to check with the city . Most areas would not have an issue building a pool . As long as everything is up to code with the city you live in . I would speak to a Contractor who specializes in Building Swimming Pools. If you have any other questions . Please feel free to reach out to me .
I agree with the other answers that it is good to start with your local city or county to see what permits are necessary. One important factor to consider is the expense of fencing the pool area. Most places will require that the pool area be secured. Another factor to include in your calculation is your home owners insurance. It is a good idea to make sure that the pool is included in case something terrible should happen.