We study a home rental market where hosts compete in prices of their listings and decide which guests to accept. We find that such screening results in inefficiently many rejections and can even reduce welfare. In a unique symmetric equilibrium, hosts randomize over prices so that it may be unprofitable for them to accept some efficient trades. Moreover, every equilibrium is inefficient when there are few hosts. We further show that introducing screening increases welfare when there are sufficiently many hosts or when the potential loss of surplus from inefficient trades is high. We discuss the implications of our findings to the online home rental platforms such as Airbnb and HomeAway.