I was accused of something that I didn't do

Yes, if law enforcement has probable cause to believe you committed a crime, you could be arrested despite being innocent.  Sadly, innocent persons can also be convicted and sentenced.  That is the reason for trials.  It forces the state to produce testimony/evidence to prove guilt.  Upon producing evidence of guilt, the accused has an opportunity, if he/she so chooses, to present testimony/evidence to try to show the state's evidence is wrong.  Unfortunately, there are numerous innocent persons who are charged and, sometimes, convicted. If law enforcement officers came to your house, they most likely were conducting and investigation because they had information that made them think you, or someone at your home, was involved in a crime or knew something about a crime even if you weren't involved.  If you believe law enforcement officers may think you had some involvement in a crime, I urge you to talk to an attorney ASAP!  You need to know your rights and how to assert your rights before deciding whether, or not, to talk to an officer or investigator.