After researching this, there does not seem to be any studied evidence that this is a major cause of hair loss. Hair loss may occur if the head garment is too tight. Also it is potentially possible for wearing a hat to cause temporary problems with hair loss, as it may restrict the proper hair air circulation to the scalp. Without this sweat may clog up the pores in the scalp and the thus new hair growth may be halted. If this is halted then hair loss can reoccur due to the natural attrition that occurs. However this effect is unlikely to be large. If this is the hair loss problem then simply stopping the hat wearing should bring the hair back, also it should be noted that for this to even potentially be an issue then the hat wearing must be constant. It is clear that the linkage between hat wearing and hair loss is at best tenuous given how many people wear hats who are not bald.
The main reason for this can be explained by the mixing up of correlation and causation, balding men will tend to want to cover up the baldness by wearing hats, but it is not the hat that is causing the baldness but rather the baldness causing the hat wearing.
Wearing a very tight hat can certainly lead to hair loss of the form of traction alopecia. This is something that Sikhs suffer from (as they are required by their religion to wear tight fitting turbans), as well as people who wear hair weaves as this continuously pulls at the hair, even certain hair styles such as deadlocking can also cause this problem. The hair loss tends to be focused around the hair line.
If you are at all concerned by this then don't wear a cap, as hair loss also has a psychological component, otherwise just make sure to get a hat which does not fit too tightly and gives the scalp room to breath.