Leasing out a house to someone without a written lease agreement is not directly "illegal" in terms of being a criminal offense, but it will have significant legal implications in other aspects that could greatly disadvantage the homeowner if problems arise later, such as the tenant not paying rent, refusing to vacate the property, or causing damage to the property.

Relevant Laws

According to the Civil and Commercial Code, Sections 537 - 571, which pertain to "Leasing."
Even without a written contract, if there is a verbal agreement and actual occupancy, it is considered that “a lease contract exists by legal relationship” (a de facto contract).