The answer depends on your interpretation of the HELOC agreement, and the threshold question would be whether that agreement defines the term “you.”
We are not aware of any laws that address whether a single co-borrower can unilaterally freeze a line of credit. Regulation Z’s HELOC rules permit you to either require the permission of both co-borrowers or to require the permission of just one co-borrower before freezing a line. Comment 5 in the Official Staff Commentary, 12 CFR 1026.40(f)(3)(vi), states:
Suspension of credit privileges following request by consumer. A creditor may honor a specific request by a consumer to suspend credit privileges. If the consumer later requests that the creditor reinstate credit privileges, the creditor must do so provided no other circumstance justifying a suspension exists at that time. If two or more consumers are obligated under a plan and each has the ability to take advances, the agreement may permit any of the consumers to direct the creditor not to make further advances. A creditor may require that all persons obligated under a plan request reinstatement.
Of course, notice of any restrictions on the line should be mailed to both borrowers. 12 CFR 1026.9(c)(1)(iii).
Many HELOC agreements include termination clauses that allow any co-borrower to freeze a line by notifying you in writing. If your loan agreement does not clearly state whether one co-borrower can freeze the line unilaterally, we believe a conservative approach would be to require both borrowers to request the freeze.