Does the imam’s room or office come under the same rulings as the mosque and should one pray tahiyyat al-masjid in it?
Question

                I am living in a room in the mosque. Do I have to pray tahiyyat al-masjid (two rak’ahs to “greet the mosque”) every time I enter it?.
Praise be to Allah.
      If the rooms attached to the mosque were built to be part 
      of the mosque, i.e., the builder of the mosque intended that they should 
      be part of the mosque in which prayers are offered, then they come under 
      the same rulings as the mosque, so the two rak’ahs for greeting the mosque 
      should be offered when entering them, and women who are menstruating or 
      bleeding following childbirth should not be allowed to stay in them. 

    But if these room are intended to be extra rooms for teaching 
    or holding meetings, or a place where the imam or muezzin lives, and are not 
    intended to be a place for prayers, then in that case they do not come under 
    the same rulings as the mosque. 

    If the intention of the one who built the mosque is not 
    known, then the basic principle is that whatever is within the walls of the 
    mosque and has a door opening into the mosque comes under the same rulings 
    as the mosque. 

    This is what may be understood from the words of the scholars 
    concerning the rooms and other facilities that are found in the mosques, 
    taking into account the differences in the situation nowadays as compared 
    with what was prevalent at the time of the earlier fuqaha’. 

    There follow some fatwas of the scholars concerning that: 

    1.

    Shaykh Ibn Baaz (may Allah have mercy on him) was asked:

    In America there is a mosque that consists of three floors. 
    The highest floor is a prayer room for women, the floor beneath that is the 
    main prayer space, and the floor beneath that -- the basement -- contains 
    washrooms, a place for Islamic magazines and newspapers, classrooms for 
    women and an additional space for women to pray. Is it permissible for women 
    who are menstruating to enter this lower level? 

    He replied: If the building mentioned was prepared as a 
    mosque and the people on the upper and lower floors can hear the voice of 
    the imam, the prayers of all people in the mosque are valid and it is not 
    permissible for menstruating women to sit in the place that has been 
    prepared for prayers on the lowest floor, because it is part of the mosque. 

    But if the lower floor was not intended by the sponsor to be 
    part of the mosque; rather he intended it to be a storeroom or a place for 
    the things mentioned in the question, then it does not come under the same 
    rulings as the mosque and it is permissible for women who are menstruating 
    or people who are in a state of impurity (janaabah) to sit there, and there 
    is nothing wrong with praying there in clean places that are not part of the 
    washrooms, like any other clean place in which there is no shar’i impediment 
    to prayer. But the one who prays there should not follow the imam who is 
    upstairs if he cannot see him or see some of the people who are praying 
    behind him, because it is not part of the mosque according to the more sound 
    of the two scholarly opinions. End quote from Fataawa al-Shaykh Ibn Baaz, 
    10/221 

    2.

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was 
    asked:

    Is it permissible to observe i’tikaaf in the rooms inside the 
    mosque? 

    He replied: That depends. The one who looks at the general 
    meaning of the words of the fuqaha’ will say that it is part of the mosque, 
    because the room that is enclosed within the wall of the mosque is regarded 
    as part of the mosque. But for the one who thinks that it was not built to 
    be part of the mosque and that it is a room for the imam, it is like the 
    apartments of the Messenger (blessings and peace of Allah be upon him). The 
    doors of the apartments of the Messenger (blessings and peace of Allah be 
    upon him) opened on to the mosque but they were (separate) houses, and the 
    Messenger (blessings and peace of Allah be upon him) did not go out to them 
    when he was in i’tikaaf. So to be on the safe side we say that the one who 
    is observing i’tikaaf should not do so in such rooms. But the people 
    nowadays usually regard rooms in the mosque as part of the mosque. End quote 
    from Sharh al-Kaafi. 

    3.

    He (may Allah have mercy on him) was also asked: What is the 
    ruling on praying tahiyyat al-masjid for one who enters the library of the 
    mosque in the following cases:

    (i)When the door of the library is 
    inside the mosque

    (ii)when the door of the library is 
    outside the mosque

    (iii)when the library has two doors, 
    one inside and one outside?

    He replied: 

    In the first case, which is when the door of the library is 
    inside the mosque, the library is part of the mosque so it comes under the 
    same rulings, and it is prescribed for the one who enters it to pray 
    tahiyyat al-masjid, and it is not permissible for one who is junub to stay 
    there unless he has wudoo’; it is valid to observe i’tikaaf there, and it is 
    haraam to buy and sell there, and all the other well-known rulings on the 
    mosque apply to it. 

    In the second case, which is when the door is outside the 
    mosque and there is no door from the library into the mosque, it is not part 
    of the mosque and the rulings on mosques do not apply to it. So tahiyyat al-masjid 
    should not be offered when entering it, i’tikaaf is not valid there, it is 
    not haraam to buy and sell there, because it is not part of the mosque as it 
    is separate from it. 

    In the third case, which is when the library has two doors, 
    one of which is inside the mosque and the other is outside: if the wall of 
    the mosque encompasses it then it is part of the mosque and the rulings on 
    mosques apply to it. If it is not encompassed by it; rather it has its own 
    separate wall, then it does not come under the same rulings as the mosque, 
    because it is separate from the mosque. Hence the houses of the Prophet 
    (blessings and peace of Allah be upon him) were not part of his mosque, even 
    though they had doors opening into the mosque, because they were separate 
    from it. 

    End quote from Fataawa al-Shaykh Ibn ‘Uthaymeen, 
    14/351. 

    And Allah knows best.