Some say no, explaining that any one word is redundant. Some say yes, like me, because I think they have different meanings.
For example: On her left hand she wore no jewellery. On the other hand, however, she had a dazzling selection of rings.
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They can certainly be used in conjunction, but unless there is a particular situation or reason for this emphasis I suspect that it will certainly feel redundant. Both connote that one thing is being contrasted with an other, and so in most cases just one will do the job of both.
I should have thought that the best situation for the phrase "however, on the other hand..." to be used is one in which a specious option or claim has been presented beforehand, and what follows will dismantle its claims. Additionally, I would think there should be some sense of the two items being complementary: there shouldn't be a "third hand" that could be considered.
As with all English, and all language, there are no rules. Only common & uncommon usages; comprehensible & incomprehensible phrases, and meaningful & meaningless expressions. At times, a seemingly redundant turn of phrase can add the specific nuance or emphasis that is called for. But I wouldn't be too quick to use it all the time.