I had a new heat pump and air handler installed. It is actually slightly undersized from what a lot have told me. I have a 1340 sq ft home with a 2 ton system. I am able to keep my house at a very low temperature but it feels damp. I went and bought a hygrometer and it has been ranging between 50 and 62% in the house. For instance right now it is at 57% and it is 61% outside. I have it at 70 degrees in the house and its about 74 out right now, not running much now at night.

I have a 19 degree temp differential across the coil so temperature does not seem to be the issue. Could the fan be going to fast and not giving it a chance to de-humidify, or is my humidity normal?

I'm in Indiana if that helps any.

Indiana can be a high humidity area and as you mentioned your unit is not pulling out enough moisture. I would drop the blower speed down to LOW and see if that helps. The slower the blower runs the longer (hang) time the air has to go through the A/C coil and the better the humidity removal.

Many years ago my shop used this principle to bring better moisture removal and comfort to the customers. I have a small diagram of the system I used to use to automatically accomplish this. Later in time I went with FanHandler components to set up a moisture removal system.

Or select low speed using relays and G terminal on thermostat.