Signatures are treated as having magical authority to create contracts.
The proverbial dotted line signature existed as an idiomatic way to convey intent to be bound to a contract as early as 1901, where it sprang up in life insurance contract advertisements nationwide, guiding insurance agents to push to have clients “sign on the dotted line” to be bound in on the contracts. The dotted line is technically unneeded, though.
Acceptance can be implied through the conduct of the offeree; anything that amounts to acceptance communicated to the other person can be grounds for forming a contract. Gordon v. Curtis Bros., 248 P 158 (Or. 1926). When you hand a dollar to a person running the farmer’s market stall, and they hand you an apple, a contract has been formed. So what then is the hubbub about with signatures?
What the Law Says
Well, there are different degrees of signature – some contracts are seen as so legally weighty that they require affirmation that the signing party understands what is being signed and is in fact the person signing; done through recordation by a notary public [these tend to be recording interests on deeds and mortgage assignments, sworn statements, advanced directives, and while only required to be “witnessed,” many wills tend to be notarized].
For lack of a better explanation, the notary process ensures that a signature on a document was placed there by a willing signer who had the present capacity to sign the documents, without coercion or fraud. For a notary’s purposes, a signature is used to indicate intent to be bound, and a signature in the notary’s journal acts as an acknowledgement that the neutral notary observed the intent to be bound.
For these contracts where a notary is required, signature is still not technically required, because a person can just manifest written assent in the manner of their choosing [e.g. thumbprints count as “signatures” under ORS 73.0401(2)(b), as a mark executed by a person with present intent to authenticate a writing].
For all other contracts, the notarization is not required, and a signature is simply a traditional form of assent. The signature occupies a strange, foggy space in contract law where expectation and reality rarely mix together. For the average consumer, the signature is a classic proof of intent to be bound. For the lawyer, the signature is merely one of many ways to show intent to be bound. For the real estate industry, many brokers treat a signature as a means of proving that the signing party was present and read the document. This disconnect of intention is fertile ground for dispute.
For example, let’s imagine you use OR Forms and your seller receives an offer. Seller rejects buyer’s offer and signs the space on the last page. The contract itself says “Seller will be bound by this Agreement only by selecting ‘ACCEPTS’ and delivering a signed copy of this Agreement to Buyer prior to the Offer Deadline.” In the hypothetical here, Seller has checked the wrong box, so acceptance clearly has not occurred. Legally, true and accurate, and there is no unambiguous indication of assent. From Buyer’s perspective, however, potentially confusing because Seller has provided two signals that seem to be going in opposite directions. Rejection ☹ and Signature☺. If the Seller forgets the checkbox because to err is human, and the checkbox is just one line in a vast contract, the question becomes even more abstract. There would be a signature and no checkbox, so on the strictest legal level, no contract is formed, but Buyer has a much stronger argument that assent was provided through Signature☺and no indication to the contrary. Signatures accompanying rejection place an extraordinary demand on the rejection checkbox [see below image for illustration of the point].

What This Means in Practice
To explain, in part where the “sign when you reject” process comes from, it can help to look at OAR 863-015-0135(3). This provision requires a licensee to maintain a written record of the date and time each written offer or counteroffer is delivered, and “if the seller rejects the offer or counteroffer, the licensee must provide a true copy to the offeror.”
A “true copy” at law is somewhat ill-defined for real estate contracts, but generally is understood as an exact reproduction of the original document that precisely replicates the content, formatting, signatures, etc. Hence, if a seller rejects the offer and the seller agent delivers a blank offer form with merely the “rejects offer” box checked, that seller agent would not be compliant. If the Seller Agent merely responds by text, “my client rejects the offer,” that would not be compliant.
The agent, when the client rejects the offer, must at the very least send the unaccepted offer back to the original offeror. There is an open question about whether checking a rejection box and signing the document results in the return of a “true copy” of the agreement, as there are material differences in the returned copy, i.e. a checked rejection box that was clearly not there before.
The rule is silent about scenarios where the client does not affirmatively reject the offer, but rather just lets it wither and expire, but there are only two possible interpretation: either (1) when an offer expires, it is not a rejection and there is no requirement that a true copy is conveyed back to the original offeror, or (2) when an offer expires, it is a tacit rejection and a true copy of the expired offer must be sent back to the original offeror.
For risk management purposes, it tends to be better to take the more protective approach and assume that even tacit rejection requires the return of a true copy.
Key Takeaway
Best practices in this situation are a different question entirely, but in this discussion, we merely approach the legal requirement: Do I have to sign my rejections? No.
At law, you are not required to sign your rejections as long as some sort of true copy returns to the offeror. Signature on the rejection line creates a direct and, at times, unnecessary reliance on contract provisions that ask the client to ignore their conditioned understanding of what it means to sign a document.