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The answer is no, they cannot, without a court order.
Understand that CPS have no "power" per se. They cannot force an interview, and they certainly cannot simply take your child away from you without a a court order. However, they have a mandate from the state to stand in front of the Court for any child that they feel is being abused/neglected.
This means that if they feel that the child is neglected/in danger, CPS may decide to take the matter to court and ask to have the court agree that your parental rights should be suspended (or even terminated in serious scenarios) until you show to the court that you are an able parent.
Now, while CPS has the "ear of the court," this does not mean that the court always agrees with DHS and if you challenge their claim, it may be denied. But this is a risk.
If CPS sees an issue, they will normally request that you do some parental classes and/or actions (such as take the children to the doctor), and if not, then they can approach the court and the court may agree that if you do not, you'd risk your parental rights being suspended.
If you feel that the requirement by CPS is unreasonable, then you can refuse. This includes the drug test. If they then go to Court (as explained above), then you'd have to show that your decision is in line with "best interests of the child."
CPS often uses misleading, cajoling, and threatening tactics, so be careful. An attorney is recommended if one decides to meet with them, because the attorney can quickly cut their attempts to intimidate the parent down.
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