Crows are very much underrated for entertainment value, most birders usually just ignore them.
They are however highly intelligent birds and fascinating to watch, the hyenas of our birdlife.
I have been watching large flocks of Lapwings, Teal, Black headed Gulls and sometimes Woodpigeons too,
in the presence of other birders, when the these birds have flushed en-masse. Every birder then quickly
searches the whole vista for a raptor or fox, I have noticed though, especially on Elton Hall Flash near
Sandbach that the agitator was often a Carrion Crow.

The crow would fly straight at a Lapwing sized bird in a flock, this bird then flushed causing the whole group
to erupt. Once the mass flock of potential prey species was in the air, the crow twisted and turned it's head
searching for a weakling to attack. Once identified the victim would be targeted, and around the Cheshire meres
I have seen them kill weak birds and enjoy a good meal, the prey species were usually Lapwings, Black Headed Gulls
or pigeons. I recently reported a Carrion Crow attacking a Snipe at Sandbach, only the small waders agility in flight
allowed it to escape.

So it is likely that if a crow sees a lone Woodpigeon, and the corvid is hungry, it will test the ability of the pigeon to
defend itself. Perhaps the crow has seen a female Sparrowhawk succeed in targeting an adult Woodpigeon, although
corvids will mob raptors to chase them away, they will always carefully watch the predator too. If there is a kill the
crow will get the scraps, or even chase off the raptor and claim the prize.

Woodpigeons have to be tough as they are a favoured prey species for numerous predators. If attacked by an opportunist
like a crow the pigeon has to prove it is fit an not an easy meal.

Regarding the intelligence of crows, I recently witnessed the interaction of a Carrion Crow and a Magpie, they would fly
at each other and peck at their opponents feet, this went on for quite a while and resulted in the corvids chasing each
other around. This certainly looked like a childs game of tag, and I could only deduce that both corvids were just having fun.
Play is something we only associate with mammals, especially young ones, so for birds to be seen indulging in having fun
really means corvids are truly special.

Wood pigeons may look defenceless, but they can suprisingly pull quite a punch with by striking out with their wings - Believe me- it can hurt alot. It's possible the crow may have been "testing" the wood pigeon or just simply teasing it. But that part I can only speculate on I'm afraid without seeing exactly what happened.