Short answer. No. The oath requirement for denying a written instrument's genuineness only applies when you appear to be a party to it. If the instrument shows a signature that was never actually yours, you do not appear to be a party to it, so you can deny its genuineness and due execution without swearing an oath.
What the law says
When an action or defense is founded upon a written instrument, or attached to the corresponding pleading as provided in the preceding section, the genuineness and due execution of the instrument shall be deemed admitted unless the adverse party, under oath specifically denies them, and sets forth what he or she claims to be the facts; but the requirement of an oath does not apply when the adverse party does not appear to be a party to the instrument or when compliance with an order for an inspection of the original instrument is refused.
Rule 8, Section 8 — How to contest such documents. Read the full provision →
The general rule: deny under oath or admit it
Rule 8, Section 8 sets a strict rule for cases built on a written instrument, such as a contract. When a claim or defense is founded on that instrument, or it is attached to the pleading, its genuineness and due execution are deemed admitted unless the other side specifically denies them under oath and states what facts it claims instead. In practice this means that if a contract is attached to a complaint and you simply ignore it or deny it in a general, unsworn way, the law treats you as having conceded that the document is genuine and was properly executed.
The exception for someone who isn't a party to the instrument
The rule carves out an exception, though, for someone who does not appear to be a party to the instrument. If your name shows up on a contract you never signed, you are, from the document's own face, being made to look like a party to it — but the rule's exception is understood to reach the situation where the person denying it is disputing that they are truly the party the instrument says they are, such as by denying that the signature on it is theirs at all. Where that is the substance of the denial, the oath requirement the general rule imposes does not apply.
The other exception: refusing inspection
A second, separate exception applies when the party relying on the instrument refuses to comply with an order for inspection of the original. If you are entitled to examine the original document and that examination is refused, you are likewise not held to the oath requirement in denying the instrument's genuineness and due execution, since you cannot fairly be expected to swear to specifics about a document you were not allowed to inspect.
What your denial still has to do
Falling within an exception does not mean you can stay silent. You still have to actually deny the instrument and, ideally, explain the basis for the denial — for instance, that the signature attributed to you is not yours — so the court and the other party understand what is actually being contested. The exceptions remove the oath requirement itself; they do not remove your obligation to raise the objection in your pleading rather than let the document pass unchallenged.