Before repainting baby furniture, check that it has not been recalled. Do this on the U.S. Consumer Product Safety Commission's website.
Purchase a lead tester to check the old paint for lead. If the furniture has lead paint, it should be destroyed or used elsewhere. According to the Methodist Hospital System, stripping it can cause the lead to leach into the wood itself.
If the old finish is lead-free, stripping is OK. The safety guidelines on RefinishFurniture.com indicate that stripping should not be done within the same air space of infants or pregnant women.
Lead-free baby furniture can be repainted as long as the paint is listed as safe for infants. The fumes may not safe for pregnant women or infants. Check the label for paint and fume toxicity.
Freshly painted baby furniture should be allowed to air out for two to three days before putting to use. Afterward, check for peeling paint on a regular basis (RefinishFurniture.com).