It depends on the previous lease
The Law
The relevant sections of the Washington code seem to be RCW 59.18.220 and RCW 59.18.650
RCW 59.18.220 provides in pertinent part that:
(1) Except as limited under RCW 59.18.650, in cases where premises are rented for a specified time, by express or implied contract, the tenancy shall be deemed expired at the end of such specified time upon notice consistent with RCW 59.18.650, served in a manner consistent with RCW 59.12.040.
(The rest of 220 deals with special exceptions for members of the US armed forces)
RCW 59.18.650 (1) provides in pertinent part that:
(1)(a) A landlord may not evict a tenant, refuse to continue a tenancy, or end a periodic tenancy except for the causes enumerated in subsection (2) of this section and as otherwise provided in this subsection.
(b) If a landlord and tenant enter into a rental agreement that provides for the tenancy to continue for an indefinite period on a month-to-month or periodic basis after the agreement expires, the landlord may not end the tenancy except for the causes enumerated in subsection (2) of this section; however, a landlord may end such a tenancy at the end of the initial period of the rental agreement without cause only if:
(b)(i) At the inception of the tenancy, the landlord and tenant entered into a rental agreement between six and 12 months; and
(b)(ii) The landlord has provided the tenant before the end of the initial lease period at least 60 days' advance written notice ending the tenancy, served in a manner consistent with RCW 59.12.040.
(c) If a landlord and tenant enter into a rental agreement for a specified period in which the tenancy by the terms of the rental agreement does not continue for an indefinite period on a month-to-month or periodic basis after the end of the specified period, the landlord may end such a tenancy without cause upon expiration of the specified period only if:
(c)(i) At the inception of the tenancy, the landlord and tenant entered into a rental agreement of 12 months or more for a specified period, or the landlord and tenant have continuously and without interruption entered into successive rental agreements of six months or more for a specified period since the inception of the tenancy;
(c)(ii) The landlord has provided the tenant before the end of the specified period at least 60 days' advance written notice that the tenancy will be deemed expired at the end of such specified period, served in a manner consistent with RCW 59.12.040; and
(c)(iii) The tenancy has not been for an indefinite period on a month-to-month or periodic basis at any point since the inception of the tenancy. However, for any tenancy of an indefinite period in existence as of May 10, 2021, if the landlord and tenant enter into a rental agreement between May 10, 2021, and three months following the expiration of the governor's proclamation 20-19.6 or any extensions thereof, the landlord may exercise rights under this subsection (1)(c) as if the rental agreement was entered into at the inception of the tenancy provided that the rental agreement is otherwise in accordance with this subsection (1)(c).
(d) For all other tenancies of a specified period not covered under (b) or (c) of this subsection, and for tenancies of an indefinite period on a month-to-month or periodic basis, a landlord may not end the tenancy except for the causes enumerated in subsection (2) of this section. Upon the end date of the tenancy of a specified period, the tenancy becomes a month-to-month tenancy.
(e) Nothing prohibits a landlord and tenant from entering into subsequent lease agreements that are in compliance with the requirements in subsection (2) of this section.
RCW 59.18.650 (2) provides a list of situations allowing a tenancy to be ended early, after various notice periods. none of these fit the situation described in the question, although 650 (2) (k) may be somewhat relevant as to what could have happened.
Analysis
Under these sections, which are part of [chapter 59.18](https://app.leg.wa.gov/RCW/default.aspx?cite=59.18}, the "Residential Landlord-Tenant Act of 1973", there seem to be several possibilities, depending on the provisions of the previous lease, but none of them seem to constitute a full automatic renewal. There are also possibilities where there was no lease, or no current lease, but these do not apply to the conditions in the question. As I read the sections, these are:
- If the lease provided that it would convert to a month-to-month or other periodic tenancy after the end of the lease period, the landlord may end the tenancy only if teh lease was for 6-12 months and the landlord gave 60 days notice (or for one of the causes in 650(2)). This is under 650(1)(b).
- If the lease does not specify that it continues indefinably or on a periodic basis, the landlord may end the tenancy only if the initial lease was for 12 months or more, or there was a series of leases each for 6-months or more with no gaps, there has not been any period of indefinite or periodic tenancy, and the landlord gives 60 days notice, or for one of the causes in 650(2). This is under 650(1)(c)(i) and 650(1)(c)(ii).
- A tenancy that was month-to-month during the covid eviction ban, but was converted to a lease within 3 months after the end of the ban, may be treated as having been on lease from its start. This is under 650(1)(c)(iii).
- Any other tenancy converts to a month-to-month tenancy at the end of any lease, unless the landlord has given proper notice or one of the causes in 650(2) applies. This is under 650(1)(d) and 220.
It is worth noticing that under 650(2)(k) if the landlord offers a new lease at least 30 days before the end of the previous one, and the terms of that new lease are "reasonable", and the tenant fails to sign the new lease but continues in possession after the end of the existing lease, the landlord may end the tenancy.
Note that section 650 provides for various cases in which the landlord "may not end the tenancy" It does not provide that in such cases the previous lease is automatically renewed. It would appear that in such cases a month-to-month tenancy begins, probably at the same rental, but the landlord may later increase rents as in any month-to-month rental.
Conclusion
So the answer to the question:
Are there similar statutes about automatic renewal of normal houses (not mobile homes)?
is: No, but tenants may not be evicted without notice except for serious cause.