I don't know where my daughter is living, how can I know my daughter is safe?

Me and my ex have joint legal custody of my 19 month old daughter. My ex was recently kicked out of her place of residence and took the baby with her. When asked where she is living she refused to tell me with whom and told me a faulty address. I told her I was filing papers with the court and she admitted to having provided a faulty address and still refuses to tell me where she is living. For all I know, god willing, she could be living in a better environment, but it's unlikely. She at one point of our conversation claimed to have gotten her own place, but her only source of income is my child support of less than $400 per month, so if this is true she is likely in a room the size of a walk in broom closet. If she's with a friend then I'd like to know who to make sure it's someone safe and that there is adequate room at the residence for the both of them. My question is how do I go about accessing her place of address? Do I call the police? I could go to the court but I ume that could take months and in the long run just ruin my kid's life in the mean time.