She teaches a variety of undergraduate and graduate courses, including physics and astronomy. Connelly regularly mentors undergraduate students in observational astronomy research, spending many nights at the RIT Observatory. She also acts as a faculty adviser for the Space Exploration (SPEX) group on campus as well as the RIT Cosplay Troupe.

Since joining the university in 2013, Connelly has been instructing innovative courses that excite students about science and encourages them to examine and develop their understanding of inclusivity, equity, and diversity. She is a recipient of the Outstanding Non-Tenure Track Faculty Award from the College of Science.

On campus, Connelly is one of the leaders of the Inclusive Excellence Initiative. The five-year, million dollar program is funded by the Howard Hughes Medical Institute and focuses on transforming faculty to better support all students, including those from non-traditional pathways. 

In and outside of the classroom, Connelly strives to create an inclusive environment where everyone can thrive. She is the founder of Rochester Women in Physics and Astronomy (ROC-WiPA), a networking group that connects and supports local women in physics. She is also the coordinator of the Rochester pod of 500 Women Scientists, which is an organization focused on making science open, inclusive, and accessible to everyone.

In recognition of her efforts, Connelly received the 2019 Isaac L. Jordan, Sr., Faculty Pluralism Award. It recognizes faculty members for their significant contributions to enhance diversity, pluralism, and inclusion within and outside of RIT.