Kilayim 9:1. If a garment is made of blended camel’s wool and sheep’s wool, if the majority is camel it is permitted [to mix with linen], and if the majority is sheep it is forbidden. Half and half is forbidden.
Yerushalmi: If a large blanket had shaatnez at one end, and that end was lying on the floor, one may still not cover oneself with the other end.
The Shulchan Aruch Yoreh Deah 301:3 brings this halacha, and the Pischei Teshuva explains that the case is when the entire blanket is sheep’s wool, and there is one thread of linen dragging on the floor. However, if the main blanket is another material, and there is a bit of wool and linen together on the edge, then it is debatable whether the entire blanket becomes forbidden. The Rambam would hold ossur, while the Rosh might hold mutar.
כלאים פרק ט, משנה א: צמר גמלים וצמר רחלים שטרפן זה בזה אם רוב מן הגמלים מותר. אם רוב מן הרחלים אסור. מחצה למחצה אסור.
ירושלמי שם: רבי ניחה בר סבה רבי יוחנן בשם רבי זעירא שאם היה בגד גדול קצתו יש בו כלאים ומונח בארץ ומקצתו אין בו לא יכסה בו מצד השני.
Rabbi Yosef Sayagh heard from a rav in Queens that a young couple once came to him for advice about their baby, who was very colicky and cried all night. Their doctor had no solution. The rav suggested that they check the baby’s blanket for shaatnez. It was found that although the blanket was not wool, it had an appliqué pattern with a picture of a teddy bear, and in that picture there was wool and linen. They removed it, and the baby stopped crying.
Source: Rabbi Yosef Sayagh
[It seems that just as we have a dispute in the laws of kashrus about whether the rule of חתיכה נעשית נבילה – a piece containing something forbidden becomes complete forbidden – applies only to milk and meat, or even to other forbidden foods (Yoreh Deah 92:4), there is a similar dispute in the laws of shaatnez. Everyone agrees that if the whole blanket is wool, and there is one thread of linen, one may not cover oneself even with the part that is only wool, because חתיכה נעשית נבילה – similar to a piece of meat cooked with milk. But if the garment is made of polyester, and only the corner has wool and linen mixed, there is a machlokes whether the shaatnez status spreads to the entire blanket.]