The study outlines the early-stage development of a free-response General Relativity Concept Inventory (GRCI), an educational instrument designed to test for conceptual understanding of General Relativity. Data were collected for the study by having 26 participants from General Relativity courses work through the questions on the GRCI. Interviews were conducted with four of the participants to gain further insight about their experience of working through the GRCI. The written responses revealed that participants were proficient when answering questions which required mathematical thought processes, but were more limited when answering questions which required conceptual and physical thought processes. The interviews revealed that participants found that free-response questions were appropriate to test for conceptual understanding of General Relativity. Participants identified that General Relativity has physical interpretations and mathematical constructs, and both are important to understand the theory. Participants thought that the GRCI could be given a formative purpose in a teaching context. The study was "proof of concept" in scope, with the aim of highlighting important points pertaining to the feasibility and development of the GRCI. Additional work to further investigate the above points highlighted by the study is encouraged.