Isn't any 12 month period equivalent to some year?
I assume the OP means by year a "calendar year", i.e. from January through to December. A "12 month period" may also start in, say, April.
ETA:
The reason the answer then may be different is that the weekdays shift one w.r.t. the days of the month in consecutive normal years (and 2 after a leap year).
The way to solve this is to write out for two consecutive years the weekdays of the 13th day of each month, starting with an arbitrary chosen weekday for January 1st of the first year, and see how many identical weekdays you find in any 12-month interval for the 13ths. Of course, you have to do this three times:
1) for two normal years
2) for a normal year followed by a leap year
3) for a leap year followed by a normal year
This doesn't answer your question, but this is a nice fact I think: (It comes from here)
I wanted to figure out how much more likely is Friday than the other days, using a computer program. The difference is not really significant, unless taking a period lasting hundreds or even thousands years long. For instance, between 1/1/1600 and 31/12/4999, the number of 13th of the month is distributed like this (from monday to sunday): 5820, 5824, 5839, 5815, 5848 (friday), 5813, 5841.In the Mathematical Gazette, vol. 53,, pp.127-129, it is shown that the 13th of the month is more likely to be a Friday than any other day.The author is a 13 year old S.R.Baxter.