What should be the declination of a star to be marginally circumpolar given the latitude & height from ground? If I'm given the latitude, I can easily find the declination by using
declination = 90 - latitude.
I can also find the angle of dip from the height but should I add or subtract it from the declination I found?
Also I have to consider atmospheric refraction but I don't know how.
Just to be clear, the "height from sea level"  (mentioned in the title) does not change what star is circumpolar. Whether the ground is at 0 units above sea level or 1500 units above sea level does not make a difference. I think what you intended to write is the height above the ground makes a difference ("angle of dip from the height" mentioned in the question). At 0 units above the ground, a circumpolar star has a declination of D1. At 1500 units above the ground, a circumpolar star has a declination that is farther from the pole, or D1-angle. (I assume that you are in the northern hemisphere.)

Refraction raises the apparent altitude of an object, so you can see a circumpolar star that is farther from than the pole than is possible without refraction. Thus, a circumpolar star has declination = D1-angle-Refraction. The adopted value for refraction of an object on the horizon is 34 arcminutes (Ref 1: The Astronomical Almanac, 2001, page A12). The actual amount of refraction depends on the atmospheric pressure and temperature. An approximate formula for refraction (applicable for observed altitudes below 15 degrees) is R=P(0.1594 + 0.0196a + 0.00002a^2)/[(273+T)(1 + 0.505a + 0.0845a^2)] where T is the temperature (degrees C), P is the barometric pressure (millibars), and a is the altitude (degrees) (Ref 1: page B62)