Yes the landlord can show the apartment provided he complies with ehe WA Residential Landlord Tenant Act which provides:
59.18.150 Landlord's right of entry -- Purposes -- Searches by fire officials -- Conditions.
(1) The tenant shall not unreasonably withhold consent to the landlord to enter into the dwelling unit in order to inspect the premises, make necessary or agreed repairs, alterations, or improvements, supply necessary or agreed services, or exhibit the dwelling unit to prospective or actual purchasers, mortgagees, tenants, workers, or contractors.
(5) The landlord shall not abuse the right of access or use it to harass the tenant. Except in the case of emergency or if it is impracticable to do so, the landlord shall give the tenant at least two days' notice of his or her intent to enter and shall enter only at reasonable times. The tenant shall not unreasonably withhold consent to the landlord to enter the dwelling unit at a specified time where the landlord has given at least one day's notice of intent to enter to exhibit the dwelling unit to prospective or actual purchasers or tenants. A landlord shall not unreasonably interfere with a tenant's enjoyment of the rented dwelling unit by excessively exhibiting the dwelling unit.
(6) The landlord has no other right of access except by court order, arbitrator or by consent of the tenant.
(7) A landlord or tenant who continues to violate the rights of the tenant or landlord with respect to the duties imposed on the other as set forth in this section after being served with one written notification alleging in good faith violations of this section listing the date and time of the violation shall be liable for up to one hundred dollars for each violation after receipt of the notice. The prevailing landlord or tenant may recover costs of the suit or arbitration under this section, and may also recover reasonable attorneys' fees.
Also, the statute says that when the landlord's or its agent's contact info is not available then the person receiving the rent becomes that agent. See RCW 59.18.060(14) which states that the landlord must:
Designate to the tenant the name and address of the person who is the landlord by a statement on the rental agreement or by a notice conspicuously posted on the premises. The tenant shall be notified immediately of any changes by certified mail or by an updated posting. If the person designated in this section does not reside in the state where the premises are located, there shall also be designated a person who resides in the county who is authorized to act as an agent for the purposes of service of notices and process, and if no designation is made of a person to act as agent, then the person to whom rental payments are to be made shall be considered such agent;Ask a similar question