There are indeed different customs regarding whether or not it is necessary / proper to recite Birkhat Hatorah prior to selichot. This clear and concise Halacha Yomit on the subject brings the major minhagim and their sources:
1) Maharshal writes that in Germany the custom was to rely on the opinion of Maharil who ruled that one need not recite the blessings of the Torah before reciting verses from the Torah in a manner of prayer and supplication- i.e. differentiating between "actual" Torah study and reciting pesukim as prayer as we do in Selichot.
2) As pertains to Ashkenazim, the Rama writes in response to the Shulchan Aruch's ruling that one should take into account the opinion that Birkhat Hatorah must be recited before Selichot, that this is not the accepted custom.
3) Rav Ovadia Yosef writes concerning Sephardim (in his Chazon Ovadia- Yamim Nora’im, page 5 and Yabia Omer Volume 9, Chapter 108) that although it seems Maran’s ruling in Shulchan Aruch to recite the blessings of the Torah before reciting verses is merely a “correct” thing to do but according to the letter of the law, Maran did not rule explicitly that one must recite the blessings of the Torah first, nevertheless, since a responsa of the Rambam (Pe’er Ha’Dor, Chapter 104) where he writes that the blessings of the Torah must be recited first was discovered after the passing of Maran, the blessings of the Torah should certainly be recited before Selichot, especially when reciting “Ashrei” at the beginning of the Selichot.