Putting a city on a river is more important that worrying about overlap, as are some other things.
Personally I'll overlap 6 tiles with my second city if I can get it on a river and sharing 3+ flood plains with my capital city... putting cottages on all the shared squares and work them quickly to towns while letting either of the cities stop work on some squares to grab GP (early great scientist with a library, maybe others with an early CoL for caste system).
I don't go too overboard with it, but an overlap isn't too big of a deal because if you get to the point where hurts your nation building, you're usually way ahead economically.
Theres even an argument to overlap as much as possible to get the highest number of cities, with the per-city bonuses from corporations. If you can get 2-3 religious HQs and a nice set of corporations (creative constructions, civilized jewelers, cereal or sushi, and maybe aluminum inc, all over a city with wall street), then theres a benefit simply from having more cities. Also getting statue of liberty helps too.