Last night we saw five couples get a score of 32 which I think is the most I have seen tied. With 13 couples still dancing it wasn't much of a problem as you still had plenty in the low 20s. When we get to the later weeks with less couples left, say 5 or 6, and they all do brilliant routines which are then marked the same how do you determine the bottom two?

Do the producers have a contingency plan for such a scenario as this, maybe do a count back, or are the judges instructed to make sure it never happens and drop a mark here or there just to make sure?

The judges scores are only half, they cannot control the final sequence. The public votes for the other half, and it's extremely unlikely that the public votes will be tied, considering there are millions (?) of them. But it is technically possible, I suppose. They must have a plan for this unlikely event.

Would they not just rely on public vote to find bottom two for dance off

It's possible, but highly unlikely. It's more possible that judges would give the same scores to everybody, which would make judges scores irrelevant and public vote alone would decide. But should that original scenario happen I think a count of public votes for each couple would decide.

I think something very close happened in one of the Christmas specials with four or five out of six couples tied, and Len then had to rank them couples from best to worst to decide their leaderboard position - but that was under the old judges' ranking position where the points would have been 6,6,6,6,2,1 instead of 6,6,6,6,5,4 like they would be today. So if such a thing were to happen now (and it is *hugely* unlikely) it's possible they'd just leave it to the public vote.

There is some explanation of Scoring (including ties) on the website (under 'About') you will have to see if it covers your example.
http://www.bbc.co.uk/programmes/arti...mrSMc8Cp/about

What can happen if there is even a partial tie in judges votes, there's a smaller point difference between those on top and bottom and a popular bad dancer can knock out a great unpopular dancer even if they would be safe otherwise.

exactly

in the event of a tie, then the public vote will come into play and the Celeb who has the least public votes would be in the dance off.