Here are selected quotations from the U.S. Supreme Court in its ruling that rent escrowing is constitutional.
We see no constitutional barrier to [the State’s] insistence that the tenant provide for accruing rent pending judicial settlement of his disputes with the lessor. The Court has twice held that it is permissible to segregate an action for possession [eviction] from other actions arising out of the same factual situation [code violations] . The tenant is not foreclosed from instituting his own action against the landlord and litigating his right to damages [for code violations]. There are unique factual and legal characteristics of the landlord-tenant relationship that justify special statutory treatment inapplicable to other litigants. The tenant is, by definition, in possession of the property of the landlord; unless a judicially supervised mechanism is provided , the tenant would be able to deny the landlord the rights of income . Holding over by the tenant beyond the term of his agreement or holding without payment of rent has proven a virulent source of friction and dispute. We think [the State] was well within its constitutional powers in providing for rapid and peaceful settlement of these disputes. Nor should we forget that the Constitution expressly protects against confiscation of private property or the income therefrom.
Lindsey v. Normet, 92 S.Ct. 862 (1972)