If the March bond future and the June bond future have the same CTD [cheapest to deliver bond] I am a little unclear on why people say that the calendar spread (long June short March) is a repo trade. Is it equivalent to selling the bond now and buying it forward?
The front and back contracts have different repo sensitivities – longer dated contracts have more repo exposures. To give you a concrete example, on the price date of March 2, 2018, if repo rates rise by 10 basis points, the price of USM2018 would rise by ~1.5 ticks, while the price of the longer dated USU2018 would rise by ~2.6 ticks. So if the repo curve rises in a parallel fashion by 10 bp, the USM8/U8 calendar spread would narrow by ~1.1 tick.
Since CTD switching is not a consideration, the calendar spread is mostly driven by repo and relative contract richness/cheapness, and you can use the numbers quoted above to think about how the spread may change when the repo curve goes up, goes down, and changes shape.