Must one wash his hands if he touched the area of the arm that he places his Tefillin?
No.<a href="#_ftn1" name="_ftnref1">[1]</a> However there are those that are stringent.<a href="#_ftn2" name="_ftnref2">[2]</a>
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<a href="#_ftnref1" name="_ftn1">[1]</a> Ben Ish Chaiy Toldos 17; Kaf Hachaim 4:99; Opinions in Piskeiy Teshuvos 27:2
This applies only to the arm which one lays Tefillin as it is normal to reveal it daily for putting on Tefillin. However the other arm, and both arms of women, are commonly always covered and hence require washing of the hand. [ibid]
<a href="#_ftnref2" name="_ftn2">[2]</a> See Piskeiy Teshuvos 27:2 for various opinions on this matter.

Shulchan Aruch HaRav | ❓Must one wash his hands if he touched the area of the arm that he places his Tefillin?

Must one wash his hands if he touched the area of the arm that he places his Tefillin? No.[1] However there are those that are stringent.[2] [1] Ben Ish Chaiy Toldos 17; Kaf Hachaim 4:99; Opinions in Piskeiy Teshuvos 27:2 This applies only to the arm which one lays