I would like to know whether I can perform Puja to Lord Shiva during menstruation period of my sister in my home?
I think, she cannot perform Puja but what about myself being a male member in her family?
As long as puja is done without any material expectations it can be done at any time and place when the mind is ready for it ☺
The physical conditions of other people at home should be immaterial. On the other hand, it may not be acceptable to other people if your sister prepares offerings which are then distributed to people. But the divine should not have a problem with it.
As per the Upanishads,
Sarvam khalvidam brahma
which includes your sister.