There are several fully (2 1/2 hours) subtitled versions of the documentary "Crimea: the way back home" on the internet:
http://sales.vgtrk.com/en/catalog/modern%20history/43450/ This seems to be the official version.
Putin made some comments about nuclear readiness at about 1:30:00 in the documentary and its context is a report about the US destroyer that set course towards Crimea, had the whole of Crimea within the firing range of its Tomahawks and reversed its course when Russia installed their Bastion anti-ship missiles on the Crimea coast as defenses. What the documentary doesn't say is that the Donald Cook only entered the Black Sea on 10 april - long after Russian control over the peninsula had been established. However, the context is still relevant as this was the point where the threat of a confrontation between the US and Russia was most acute. Further in the documentary it is also mentioned that when the Donald Cook was withdrawing from the neighborhood of Crimea some Russian fighter planes flew closely over it. This may well have been a warning that - even outside the range of the Bastion system - it shouldn't do foolish things on Crimea.
Here a transcript of the relevant section. This is from the Liveleak version and not the official translation so it may be wrong on some details:
Q: When you talked with Western leaders was it clear to you right away that there wouldn't be any military interference from their side?
A: Of course not. This couldn't be clear right away. That's why, at the first stage, I had to give certain directions to our armed forces - not only directions but direct orders - about the possible actions of Russia and our armed forces in any possible events.
Q: Do your words imply that our nuclear forces were also put on standby?
A: We were prepared to do that. I talked to the colleagues, and I was open with them, as I am with you now. This is our historic territory. There live Russian people. They are in danger now. We can't leave them alone. It was not us who staged the coup.It was done by the nationalist and the people with far-right views.
You supported them. But where do you live. Thousands of miles away.
But we live here - this is our land. What do want to fight for there? You don't know, do you? But we do know, and we are ready for it. This is an honest and open position. That's the way it is.
So I don't believe anyone wanted to fan some world conflict out of it. But we were not looking for a fight. There simply forced us to take these actions. And I repeat, we were ready for the worst case scenario. But I presumed that it wouldn't happen. It was unnecessary to aggravate the situation too much.
Commentator: Later, in the Ministry of Defense, we were told that at that time some military experts has suggested Vladimir Putin as Commander-in-Chief to use all available means to demonstrate that Russia was ready to protect its national interests. The president replied: although the situation is complex and dramatic, the Cold War is over, and we don't need international crises like Caribbean. Moreover, the circumstances do not require such actions and it would run contrary to our own interests.
As for our nuclear deterrence forces - added the president - they are always on standby anyway.