Did Laverne and Shirley ever have a romantic connection?

No, Laverne and Shirley never had a romantic connection. Although the two were incredibly close friends, the show never explored a romantic relationship between them. The showrunners were adamant that their relationship remain strictly platonic, as they wanted to showcase the bond of female friendship without introducing any romantic elements. Throughout the show, there were occasional hints that the two might be interested in each other, but these were quickly dismissed. Laverne and Shirley were portrayed as two independent women who could rely on each other without the need for romance. Their bond was one of close friendship, respect, and mutual understanding, which is why the show was so popular and beloved by many.