I had heard about the same thing you have, but my answer is always, "Is that something that the church actually teaches, or is it just something that some people do because they are hurting and in desperate need of healing?
I did some checking and according to
Approved Apparitions* El Negritta *is not approved by the church even though Costa Ricans consider her their patron saint. I don’t know of any healings there, but I suppose it’s possible.
As for the whole devotion and seeking it for healing (from God, remember), I would have to say that it is not much different than what we find in the New Testament in
John 5:4 (But be sure to scroll down and read the note which points out that that verse is not in Catholic Bibles and yet is included in most of the n-C ones. Obviously there’s a reason…but in this case we see a passage that relates to this kind of instance in the n-C Bible, their ultimate and final authority. So… what can they say?
- 5:4] Toward the end of the second century in the West and among the fourth-century Greek Fathers, an additional verse was known: “For [from time to time] an angel of the Lord used to come down into the pool; and the water was stirred up, so the first one to get in [after the stirring of the water] was healed of whatever disease afflicted him.” The angel was a popular explanation of the turbulence and the healing powers attributed to it. This verse is missing from all early Greek manuscripts and the earliest versions, including the original Vulgate. Its vocabulary is markedly non-Johannine.
Also see Acts 5:
12] Now many signs and wonders were done among the people by the hands of the apostles. And they were all together in Solomon’s Portico.
13] None of the rest dared join them, but the people held them in high honor.
14] And more than ever believers were added to the Lord, multitudes both of men and women,
15] ** so that they even carried out the sick into the streets, and laid them on beds and pallets, that as Peter came by at least his shadow might fall on some of them. **
16] The people also gathered from the towns around Jerusalem, bringing the sick and those afflicted with unclean spirits, and they were all healed.
Again…kinda weird, but yet it happened and is right there in the Bible, big as life.

How is that much different than the El Negritta devotion? Those people know it’s not the statue doing it just as the people looking for healing in the scriptural cases knew where the healing power was coming from.
Another thing to consider is the fruits of this.
Look up
Matthew 7:15-20. What is the fruit of this devotion? Increased faith in God and love for Our Lord and His church and seeking His healing power, right? So based upon that, though it is extreme, how does it fail the test of Christian faith and practice. It doesn’t…
Hope this helps