M ex girlfriend is accusing me of sexual assault. Can she give police permission to search the apartment? She had just moved in but was not on the lease or receiving mail at the apartment. She nor I was at home at the time the police came. Can police legally enter and remove items without a search warrant under these circumstances?
You failed to provide the name of your state, and some of these laws might vary by state.
But, if she is a resident and has dominion and control over the items and rooms in question, she can generally give consent to search and even to seize items. If you objected you could have declined and forced them to obtain a warrant. But, if you were not there to object, you would then be left with having to go for a 'Hail Mary' and ask your attorney to make a motion to suppress the evidence arguing she did not have the authority to grant consent or to turn over property that it yours and yours alone. But, since the two of you were living together, and assuming she was living with you at the time she invited the police in, such a motion would likely fail.
If you have been charged with a crime, consult legal counsel ASAP.