Yes, you do
As clarified by Sean K. Reynolds (ex-developer at Paizo):
On page 66 of Ultimate Equipment, I see we have a holy symbol in the form of a tattoo on your body. Does this allow you to not need a free hand manipulating a divine focus when casting a spell?
Correct; that's the point of getting the tattoo. Of course, if you try to infiltrate an evil cult, you're gonna have some 'splainin' to do...
Here, his answer was addressing spells, but the tattoo works as a holy symbol to channel energy as well.
Holy Symbol, Tattoo In some religions, you are allowed to tattoo or brand your deity’s holy symbol onto your skin (typically the palm, back of the hand, or forearm) in a special ceremony. Thereafter, it functions like an actual holy symbol of your faith, and you may use it as a divine focus for spellcasting, channeling energy, and so on. The tattoo must be fully visible to use it in this way (it cannot be covered with a glove, gauntlet, or any other material). The listed price includes the cost of a simple brand or non-fading black tattoo; add appropriate tattoo costs if you want something more elaborate. Specifically damaging or erasing the tattoo or brand negates its use as an actual holy symbol.
Mr. Reynolds's post is linked every time this question shows up at Paizo's messageboards. But there are many other ways to avoid having a free hand to manipulate or present your holy symbol, such as the Birthmark trait, the Create Reliquary feat, and Iomedae's Magic Shield, the Blessed Hammer feat for followers of Torag, or even the Sacred weapon enchant, to name a few. The tattoo is merely another method that may be cooler.