I abstractly answer the following questions without exploring your factual circumstances:
Q1: Does it infringe the state government's trademark rights to use a photo that shows a state government's logo?
The essence of trademark law is to prevent consumer confusion of the source of the product/service. Therefore, even assuming that the logo is a valid trademark of the state government, using the trademark in a way that clearly does not cause consumer confusion in general does not infringe the owner's trademark rights.
Q2: Does it infringe copyright to use the said photo in Q1, even though the photo is purported to be under public domain?
Logos are usually copyrighted. With some exceptions, using a copyrighted image in a commercial setting without permission likely infringes copyright. Nevertheless, many state governments put their works under public domain. If so, there can't be copyright infringement.