leaking bath tub drain

Hi. The drain in my bath tub leaks water, but let me paint the scenario for any advice, suggestions.
When we take a shower, the drain does not leak and drains properly.
If we run water as in taking a bath, but leave the drain open, it does not leak water.
If we close the drain, and fill up the tub with water as if taking a bath, I believe the water is leaking out around the drain, where the chrome flange-like part lays against the body of the tub. The amount of water has to be almost to the point of where the water reaches the overflow valve. If it is just a little, it doesn't leak. I tested my theory, and to make sure our porcelain tub was not cracked by buying a rubber sink stopper (flat piece of rubber) and laying it over the drain, with the tub full. The water did not leak into the room below (our den). I think I may need new plumbers putty around the drain, where it meets the bath tub, so finally here is my question:
How do I get the piece of the drain with the metal, chrome flange-like part up, or how do I unscrew it so I can place plumbers putty underneath it? I've done this with my bathroom sink, but didn't if a bathtub was similar. I do not have access to the bottom of my tub, so is there a way it can be done from on top, as in the tub or would it have to be done from below the tub. Thanks for reading my message and any help you can give. Eric Swope

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