All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to greet one person, male or female, with the wording “Assalaamu Alayk”, and this is mentioned several times in the Sunnah, but you have to say “Assalaamu ‘Alayka” when addressing a male and “Assalaamu ‘Alayki” when addressing a female [as per the Arabic language grammar].
However, it is better to use the plural form of greeting [i.e. Assalaamu ‘Alaykum] even if you are greeting one person only. Ibn Muflih quoted An-Nawawi as saying: “It is desirable for the person starting the greeting to say: “Assalaamu ‘Alaykum wa Rahmatullaahi wa Barakaatuhu”, greeting in the plural form even if there is only one person greeted, and the person who answers the greeting should say: “Wa ‘Alaykum Assalaam wa Rahmatullaahi wa Barakaatuhu”.
Nevertheless, it is acceptable to say “Assalaamu ‘Alayk” when addressing a male or a female.
Finally, it should be noted that it is disliked for a Muslim man to greet a girl with Salaam if she is not his wife or his female Mahram, and it is also disliked for her to respond to him, and it is also disliked for her to greet him with Salaam and for him to respond to her with Salaam, as this is a means of temptation (for both of them) as stated by the jurists .
Allaah Knows best.